Percentage rates of investments: Interpreting them correctly

percentage rates of investments

Percentage rates appear to be popular in many financial publications. We see them in different forms- either positive or negative. As investors, some common areas we find percentage rates interesting are documents that deal with investment returns or profits. Many investors, as well as prospective ones, look out for rates quoted by financial institutions to make informed decisions. Unfortunately, most prospective investors get confused in the interpretation of these rates. Besides the misinterpretation of percentage rates, others naively compare rates associated with different investment categories. Their naivety reflects in the manner they query or make statements such as:

  1. “Which mutual funds have the highest interest rates?”
  2. “Which stocks have high interest rates?”
  3. “The interest rate of Mfund [money market fund] is higher than that of Epack [equity fund]”

One consequence of misinterpreting percentage rates is the disappointment that follows when lower-than-expected returns are made on an investment. During a chat with John (a follower of Sikasεm) a few days ago, I was not surprised when he expressed the frustration he had recently been through. He revealed:

“I nearly cried when 700 cedis in an account yielded only 4.57cedis.”- John Mensah

I understand many more people have had such an experience before. Yes! It is a very painful experience to go through. However, to avoid or reduce the impact of similar painful experiences, it would be worthy to study a few of the percentage rates we usually come across in investment products.


Annual interest rate

The most common investment products that make use of annual interest rates are Treasury bills and fixed deposits. The interest rates quoted on the various Treasury bills and fixed deposits are annually-based. That is, the return or profit earned on these investment products, when utilising the quoted interest rates, is for a period of one year (12 months). However, T-bill investments do not always mature in 12 months. For instance, the 91-day and 182-day T-bills mature after three months and six months respectively. Hence, the calculated interests need to be prorated (distributed) for the actual maturity periods. That is three months and six months for the 91-day and 182-day T-bills respectively.

To be clearer on this, let’s go through the sample calculation below.

     How to calculate Treasury bill interest

Let’s assume that you invest GH¢1000 at the current 91-day T-bill rate of 13.4700%,

Now, since the quoted interest rate (13.4700%) is an annual (12-month) rate, the total interest on the GH¢1000, after 12-months, would have been (1000×0.1347) = GH¢134.7


However, 91-day T-bill investment matures after three months. Hence the above total interest needs to be prorated for a three-month investment period.

Thus, the real interest to be earned on the GH¢1000 would be (1000×0.1347)/4 = GH¢33.675

Note that 3 months × 4 = 1 year. That is why you see the total (annual) interest being divided by 4

In a similar manner, the annual interest would have been divided by 2 if it were to be 182-day (6 months) T-bill investment.


Another means to estimate your T-bill or fixed deposit interest is to first distribute the calculated annual interest per each month and further multiply the monthly interest by the actual number of months the money stayed invested.  Using the same example above, the interest earned per month would be (1000×0.1347)/12 = GH¢11.225 Remember that there are 12 months per annum (year).

Now, since the money is being invested for 3 months (91-day T-bill), we multiply the monthly interest figure by 3. That is, (GH¢11.225×3) = GH¢33.675


Annual yield

Annual yield is the annual rate of return on an investment, taking into consideration the compounding effect of any intermediary interest earned. Annual yield is most often reported as the investment return on money market funds (a pool of fund invested in fixed income products). Managers of money market funds, while estimating the annual yield, assume that the funds would remain intact in the account for one year (365 days). For instance, the estimated annual yield of HFC Unit Trust on 10th May 2017 was reported as 20.31%. What this means is that assuming the funds in HFC Unit Trust remain intact from 10th May 2017 to 10th May 2018 (one year), the estimated rate of return would be 20.31%. That is, the value of the mutual fund would appreciate by 20.31%. However, since investors continue to deposit and withdraw from mutual funds, the funds are therefore not expected to remain intact throughout the full year. Thus, fund managers keep revising their annual yield on a daily basis to reflect the changes. For this reason, it may be difficult to precisely calculate the return on a mutual fund (money market) investment over a period.

Due to the effect of compounding, investment returns associated with money market funds may not be evenly distributed over the investment duration. Let’s assume that you had invested GH¢1000 in Databank’s Mfund on 12th May 2017. Annual yield of Mfund on 12th May 2017 was 19.88%. Thus, the estimated return (profit) on the GH¢1000 after one year would be (GH¢1000×0.1988) = GH¢198.8 However, the GH¢198.8 takes into account the compounding effects of intermediary profits that are reinvested by the fund managers. As such, it cannot be equally distributed by each of the 12 months. This implies that if the GH¢1000 stays invested for just six months instead of the 12 months, you cannot expect to earn half of the annual profit.

Once again, let’s go through another example using real historical data.


Table: Historical investment value of an Mfund account

Date Mfund value, GH¢ Monthly return, GH¢
30/09/2016 879.41 —–
31/10/2016 894.71 15.3
30/11/2016 912.03 17.32
31/12/2016 928.61 16.58
31/01/2017 945.83 17.22
28/02/2017 958.98 13.15
31/03/2017 971.49 12.51
30/04/2017 988.82 17.33


The table above shows the value of an Mfund investment account (a money market fund) over a seven-month period. Based on the investment values, the monthly returns are also calculated by subtracting preceding values from current ones.

Even though the fund manager (Databank) had estimated an annual yield of about 23% at the time, the returns (as seen in the table) were not equally distributed over the period- They differed from one month to another. For instance, November return of GH¢17.32 had increased from the October return of GH¢15.3. On the other hand, the return in January (GH¢17.22) had dropped to GH¢13.15 in February. Factors that account for non-equal distribution of Mfund returns include, but not limited to, compounding effect of intermediary profits as well as changes in interest rates of fixed income products during the investment period.


Year to date return (YTD)

Whenever we mention year to date, we refer to the period between the start of a calendar year and the present date of the same year. The beginning of the calendar year often has 1st January as the baseline. Year to date return therefore refers to the return or profit made so far, from 1st January to the present day of the calendar year. For instance, a year to date investment return of 10%, as of 30th April 2017, implies that from 1st January to 30th April 2017, a return of 10% had been made on the investment.

Year to date returns are usually reported on equity-related investment products such as the Ghana Stock Exchange (GSE), Epack investment fund, SAS fortune fund and HFC Equity Trust. Similar to the annual yield explained earlier, year to date returns can drop or increase from time to time within a calendar year. Again, year to date returns do not accumulate in a linear functional manner. In other words, they do not distribute proportionally along the calendar year. The mere fact that a year to date return after the first four months (30th April) was 10% does not necessarily mean that the return at the end of the year (31st December) would be 30%. This is due to price fluctuations on the equity markets. On every business day, equity fund managers recalculate their year to date returns based on the present prices of stocks.

It is also important to note that published YTD returns mostly affect existing shareholders than prospective ones. Now let’s have a look at the scenario below:

percentage rates of investments_scenario

From the scenario above, it is clear that the investor lacked understanding of YTD returns. This is a common mistake many prospective investors make when investing in equity funds. As I mentioned before, YTD returns mostly affect existing shareholders. Thus, the 45% the prospective investor noticed in September 2016 was a profit that had been ‘earned’ already by the existing shareholders of the equity fund. To accurately estimate his return, he needed to do that in reference to September 2016 since that was when he made the deposit. According to the scenario, the fund had lost 5% (45% to 40%) from September to December. Hence, the investor had actually lost part of his deposit.

In a similar situation, an existing shareholder who topped up his account in September 2016 would not enjoy profit on the additional deposit that was made in September. Nevertheless, he would enjoy the 40% return on his previous investment (prior to the deposit in September) if that investment had stayed in the equity fund from January to December 2016.


Comparing percentage rates

It is important not to compare percentage rates of different categorical investments. For example, the annual yield of HFC unit trust (a money market fund) as of 10th May 2017 was 20.31%. On the same day, the year to date return on HFC equity trust (an equity mutual fund) was 9.68%. It would be a big mistake to compare these two percentage rates and assume that HFC unit trust performs better than HFC equity trust. This is because the 9.68% return on HFC equity trust is only for the period of 1st January 2017 to 10th May 2017 while the 20.31% on HFC unit trust is a 12-month estimated rate.

On another note, it may not be appropriate to compare the year to date (YTD) returns of two different equity funds in the early part of a year. As stated earlier, YTD returns do not distribute proportionally along the calendar year. For instance, the YTD returns of SAS fortune fund and Epack investment fund, as of 11th May 2017, were 14.51% and 5.4% respectively. While the rate for SAS fortune fund is higher than that of Epack, it may be premature to conclude that SAS fortune fund performs better than Epack investment fund. This is because the YTD return of SAS fortune fund may drop while that of Epack can rise steeply before the year ends. Thus, a more appropriate comparison could be done at the end of the calendar year.

Treasury bill vs. mutual fund: “Instead of mutual fund, why not T-bill?”

treasury bill vs. mutual fund

Treasury bill is noted as one of the most popular investment products globally, mainly due to its simplicity and low-risk nature. However, the proliferation of mutual funds, particularly money market funds, has led to diversion of some investors from T-bills. Some questions still remain unanswered regarding Treasury bill vs. mutual fund investment. Such questions are similarly raised by well-informed investors as well as potential investors who wish to make good choices in their investment decisions.

Just about a week ago, I happened to have a discussion with one of Sikasεm’s followers. After almost an hour chat with Kenneth, he asked:

“If you were going to invest in an Mfund, why not just buy a treasury bill?”

The argument centred on the fact that managers of money market funds invest collected pool of money in fixed income securities such as T-bills. As such, won’t it be logical for investors to buy the T-bills rather? While Kenneth’s argument appears laudable, both T-bills and mutual funds have their own pros and cons that must be carefully reflected on (Note: ‘mutual fund’ as used in this write-up refers to money market funds in general).


  1. Treasury bill vs. mutual fund: Unlike T-bill, an investor can regularly top up the same mutual fund account

As it stands now, it is not allowed to top up an existing T-bill investment with additional funds. For instance, you may have invested GH¢200 in a 91-Day T-bill a month ago and wish to top up the existing GH¢200 with an additional GH¢100 to form a single investment of GH¢300. This would not be possible due to the differences in interest rates and maturity dates. In other words, the initial GH¢200 would be maturing at an earlier date with a different interest rate. As you may be aware, interest rates of T-bills keep changing week by week.

Let’s assume that the GH¢200 you invested a month ago had an interest rate of 18%, maturing on 14th April 2017. Now, interest rate of 91-Day T-bill has dropped to about 15%. Besides, any money invested in a 91-Day T-bill today would be maturing after three months. This makes it difficult to combine the subsequent GH¢100 with the GH¢200 invested earlier on. You may therefore have to invest any new fund (in this case, the GH¢100) separately. Thus, you would be having several T-bill investments for the various additional funds that would be maturing on different dates.

The situation is different for mutual fund accounts since you can top up with any amount at any time. An investor can make a regular contribution to his mutual fund account to suit his needs. A mutual fund may be therefore ideal for investors who choose to consolidate their fixed income investments in a single portfolio.


  1. Treasury bill vs. mutual fund: The yield on mutual funds general exceeds that of T-bills, even though slightly

Historically, the yield on mutual funds appears to be slightly better than that of T-bills. Detailed comparison of historical data of mutual funds and T-bills can be found in the post below:

Performance comparison of mutual funds in Ghana

There are a number of financial institutions that pay higher than the prevailing market rates. These institutions however require a minimum investment amount that outweighs the financial capability of many individual investors. As institutional investors, mutual fund managers are able to raise such minimum bids to earn the attractive rates. This is one of the reasons why mutual funds generally perform better.


  1. Treasury bill vs. mutual fund: Commissions are paid on mutual fund accounts but not on T-bills

Investing in T-bills come with no charges. Authorised dealing institutions are paid commissions by the Bank of Ghana (the originator of T-bills). Thus, the investor pays no further charges. On the other hand, mutual fund investment comes with varying fees and commissions. For details on investment fees and commissions, refer to the post below:

Investment costs in Ghana: Understanding the fees and commissions

Due to the fees and commissions charged on mutual funds, an investor may need to stay invested for a while in order to cover the charges and subsequently earn some reasonable returns. For instance, most mutual funds charge upfront fees of 1% of the invested money. Let’s assume that three investors decide to invest GH¢500 each in one of such funds. The fund manager would therefore charge each investor GH¢5 (that is 1% of GH¢500). Now, out of the three investors, one would like to withdraw his money after just a month. The other two investors decide to stay invested for one year. In effect, since each investor was equally charged GH¢5, the investor who pulls back earlier after just a month appears to be paying more in fees. In other words, he pays a fee of GH¢5 for just a month of investment while the others pay GH¢5 for the whole year.


  1. Treasury bill vs. mutual fund: T-bills are safer

As far as risk is concerned, both T-bills and mutual funds (money market funds) can be considered safe. Nevertheless, T-bills appear to be safer since they are issued by the Government. It is nearly impossible for the Government to run away with investors’ money. However, the same cannot be said of the various private financial institutions that manage the mutual funds.


  1. Treasury bill vs. mutual fund: Mutual funds may require less monitoring and tracking

Since mutual funds are constantly managed by experts, investors may not be required to keep track of matters such as changing trend of interest rates, which short-term instrument to buy, which ones are maturing, which ones must be rolled over, etc. Such monitoring and decisions are taken care of by the mutual fund managers.

T-bill investors, on the other hand, must have dedicated time to keep track of their investments and make the right buying and selling decisions. This is necessary, especially if they have different funds maturing on different dates. Even though some financial institutions send notifications to remind investors of their T-bill maturity dates, many others do not send any notification.  T-bill investors would therefore need to keep track of their investments’ maturity dates in order to give any further instructions to their banks.


  1. Treasury bill vs. mutual fund: Payments of interests on T-bills are simpler and well-defined

Since there is no maturity date for mutual funds, investors who wish to use their investment as a regular income source (eg. monthly payments) may always have to fill a withdrawal instruction form on a regular basis. This is however not the case for T-bills whereby the investor is paid the interest in his account upon maturity. T-bill investors need not to fill any additional withdrawal form unless they want to prematurely terminate their investment.

The defined interests on T-bills further make financial planning easier. Before you invest your money in a T-bill, you’re assigned a defined interest rate which does not change until the investment matures. This is beneficial for investors who want to plan ahead precisely.

The yield of mutual funds however changes in line with the prevailing interest rates of fixed income securities. If you’ve had taken a keen look at the annualised yields of mutual funds, you would realise that they fluctuate almost every day. For instance, since the beginning of this year (2017), the annualised yield of Databank Mfund has kept fluctuating between 22% and 20%. A defined annualised yield of mutual funds can only be known at the end of the financial year (31st December). Hence, investors whose planning are based on today’s rate may be slightly disappointed in the course of time.

Again, Treasury bill interests can be discounted, unlike mutual funds. What this means is that the interest calculated on T-bills can be given to investors in advance, even before their invested money matures. Discounted rates are slightly lower than the normal interest rates.


  1. Treasury bill vs. mutual fund: Mutual funds offer investors the opportunity to diversify their fixed income portfolio with smaller amounts

Proper diversification is one of the important characteristics of a prudent investment strategy. Since mutual fund managers invest across varying fixed income securities, investors, by default, have their investments diversified on their behalf. This is irrespective of the amount a mutual fund investor holds. For example, ‘investor A’ who invests GH¢100 will have the same diversification pattern as ‘investor B’ who invests GH¢500. Thus, investors with smaller amounts are equally offered the opportunity to diversify their fixed income portfolio.

On the other hand, most financial institutions demand some minimum amounts for T-bills purchase. For instance, information on Databank’s website shows that a minimum amount of GH¢500 is required for their T-bills purchase. This limitation may restrict low-income investors who wish to diversify. Let’s assume that you have GH¢500 but would like to purchase a variety of short-term securities comprising of 91-Day T-bill, 182-Day T-bill and probably a fixed deposit investment. With the minimum purchasing limit of GH¢500, your GH¢500 could only buy you a single short-term security. In effect, you may not be able to diversify as you had originally intended to.

Treasury bill investment: Choosing between 91-Day, 182-Day & 1-Year Note

treasury bill investment

Treasury bill investment has not been something new to the investing public. Being one of the most safest and liquid form of investment products, it has become one of the first products to come to mind when one wants to invest.

We may all have been aware of the different Treasury bill investment terms (or periods) issued by the Government of Ghana, the common ones being the 91-Day term, the 182-Day term and the 1-Year Note. Each Treasury bill term is issued with a different interest rate which keeps changing week by week. As investors, we generally seek for high returns or interest rates on our investments (considering risks of course). However, have you ever thought of this question before?:

Which of the Treasury bill investment terms will yield more profit if invested in?

Well, if you have thought about this before, then I guess we share a common thinking 🙂 at least on this one. But wait! We’re not alone. Many others have similarly queried whether the 91-Day term, the 182-Day term or the 1-Year Note should be the ideal Treasury bill investment term when it comes to profit. To answer this query, we may need some data over a certain period, preferably over a reasonable period. Using historical data of Treasury bill rates, we tried to find out the different profits one would have made if he had invested exclusively in each of the Treasury bill terms throughout a particular year. For simplicity, we used GH¢ 1000 as a starting principal for all scenarios.

For instance, within the same calendar year,

Scenario 1: How much profit would one make if he had invested GH¢ 1000 exclusively in a 91-day Treasury bill throughout the year?

Scenario 2: How much profit would one make if he had invested GH¢ 1000 exclusively in a 182-day Treasury bill throughout the year?

Scenario 3: How much profit would one make if he had invested GH¢ 1000 exclusively in a 1-Year Treasury bill note?

From the three different scenarios, we compared to find out which would have been more profitable. This analysis was done using historical data for the past four (4) years. That is, from 2012 to 2015. The results from the analysis may guide investors when deciding on Treasury bill investment.

See also: Treasury bill versus Dollar holding: A performance comparison

Treasury bill investment- Historical data

The tables below show some historical data of Treasury bill for four (4) calendar years (2015, 2014, 2013 & 2012). As mentioned earlier, our main motive was to find out which of the Treasury bill terms would have yielded more profits if one had invested exclusively in it throughout a particular year.

Using 2015 as an example, investing exclusively in a 91-Day Treasury bill term (starting from 05/01/2015) would require a roll-over of the invested capital after every three months. That is, a roll-over on 06/04/2015, 06/07/2015 and finally 05/10/2015.

Similarly, investing exclusively in a 182-Day Treasury bill term (starting from 05/01/2015) would require a roll-over of the invested capital after six months (06/07/2015).

However, investing exclusively in a 1-Year Note would require only a one-time investment on 05/01/2015.


Date Treasury bill rates, %
91-Day 182-Day 1-Year Note
05/01/2015 25.8385 26.4077 22.5
06/04/2015 25.2039
06/07/2015 25.1978 25.8819
05/10/2015 25.3026
04/01/2016 22.7939 24.3574 23
Date Treasury bill rates, %
91-Day 182-Day 1-Year Note
06/01/2014 19.233 19.1813 17
07/04/2014 23.9862
07/07/2014 24.1023 22.3453
06/10/2014 25.7118
05/01/2015 25.8385 26.4077 22.5
Date Treasury bill rates, %
91-Day 182-Day 1-Year Note
07/01/2013 23.0275 22.9947 22.9
08/04/2013 22.9829
08/07/2013 23.0715 23.0314
07/10/2013 20.623
06/01/2014 19.233 19.1813 17
Date Treasury bill rates, %
91-Day 182-Day 1-Year Note
16/01/2012 10.82 11.09 11.25
16/04/2012 13.85
16/07/2012 22.3415 22.9123
15/10/2012 23.1219
14/01/2013 22.9117 22.7443 22.9

Treasury bill investment- Interest earned on GH¢ 1000

In the tables below, you will find the various interests or profits earned on investing GH¢ 1000 exclusively in each of the Treasury bill periods.

This was done in two categories. First, we calculated the total profits earned when one does not reinvest any of the intermediary profits accrued within the particular year.

In the other category, we calculated the total profits earned when one reinvest all intermediary profits accrued within the particular year.

Note: All calculated profits are in Ghanaian Cedis (GH¢)


Category 1: Interest earned on GH¢ 1000 with no reinvestment of intermediary profits

2015- Interest earned on GH¢ 1000 
91-Day 182-Day 1-Year Note
1st month 0 0 0
3rd month 64.60 0 0
6th month 63.01 132.04 112.50
9th month 62.99 0.00 0.00
12th month 63.26 129.41 112.50
Total profit 253.86 261.45 225.00
2014- Interest earned on GH¢ 1000 
91-Day 182-Day 1-Year Note
1st month 0.00 0 0
3rd month 48.08 0 0
6th month 59.97 95.91 85.00
9th month 60.26 0.00 0.00
12th month 64.28 111.73 85.00
Total profit 232.58 207.63 170.00
2013- Interest earned on GH¢ 1000 
91-Day 182-Day 1-Year Note
1st month 0 0 0
3rd month 57.57 0 0
6th month 57.46 114.97 114.50
9th month 57.68 0.00 0.00
12th month 51.56 115.16 114.50
Total profit 224.26 230.13 229.00
2012- Interest earned on GH¢ 1000 
91-Day 182-Day 1-Year Note
1st month 0 0 0
3rd month 27.05 0 0
6th month 34.63 55.45 56.25
9th month 55.85 0.00 0.00
12th month 57.80 114.56 56.25
Total profit 175.33 170.01 112.50


Category 2: Interest earned on GH¢ 1000 after reinvestment of intermediary profits

2015- Interest earned on GH¢ 1000 after reinvestment of intermediary profits
91-Day 182-Day 1-Year Note
1st month 0 0 0
3rd month 64.60 0 0
6th month 67.08 132.04 112.50
9th month 67.22 0.00 0.00
12th month 67.51 146.50 112.50
Total profit 266.40 278.54 225.00
2014- Interest earned on GH¢ 1000 after reinvestment of intermediary profits
91-Day 182-Day 1-Year Note
1st month 0 0 0
3rd month 48.08 0 0
6th month 62.85 95.91 85.00
9th month 64.04 0.00 0.00
12th month 68.40 122.44 85.00
Total profit 243.37 218.35 170.00
2013- Interest earned on GH¢ 1000 after reinvestment of intermediary profits
91-Day 182-Day 1-Year Note
1st month 0 0 0
3rd month 57.57 0 0
6th month 60.76 114.97 114.50
9th month 61.18 0.00 0.00
12th month 54.71 128.40 114.50
Total profit 234.23 243.37 229.00
2012- Interest earned on GH¢ 1000 after reinvestment of intermediary profits
91-Day 182-Day 1-Year Note
1st month 0 0 0
3rd month 27.05 0 0
6th month 35.56 55.45 56.25
9th month 57.84 0.00 0.00
12th month 61.15 120.91 56.25
Total profit 181.60 176.36 112.50


From the results, it can be noticed that investing GH¢ 1000 exclusively in either a 91-Day or 182-Day Treasury bill period yielded more profit than investing the same amount in a 1-Year Note. This observation applies for both categories ie. whether reinvesting intermediary profits or not.

The above conclusion may be attributed to the fact that money invested in a 1-Year Note attracts a fixed interest rate until one calendar year before it could be invested again with the prevailing (new) interest rate. On the other hand, money invested in a short term Treasury bill (91-Day or 182-Day period) normally enjoys a gradual upward change in interest rates within the calendar year.

Comparing the profits earned on the 91-Day and 182-Day terms, an interesting cyclical kind of observation could also be made. While the 182-Day Treasury bill earned more profit in 2015 and 2013 than the 91-Day Treasury bill, the 91-Day Treasury bill, on the other hand, yielded more profit in 2014 and 2012 than the 182-Day Treasury bill.

So, here we are. Locking up our money in a long-term treasury bill investment such as the 1-Year Note may not be the right choice. Instead, short term treasury bill investment, such as the 91-Day term, offers a high possibility of yielding more profit.