On Sipho’s sixteenth birthday, his mother gives him R1000. He decides to invest it in a savings account that pays an annual interest rate of 6.3% p.a. compounded annually. He wants to have some pocket money in two years’ time when he’s doing his first year at university. Let’s work out how much he is going to have at the end of 2 years.
We need to write down what important information we are given in the statement.
Principal amount = R1000
Interest = 6.3% per annum. This means that at the end of the first year Sipho earns an additional 6.3% on his original investment. And at the end of the second year he earns 6.3% of the amount he accumulated the previous year. For calculation purposes, let’s convert 6.3% into a fraction i.e. 6.3/100 = 0.063.
NB: Unlike simple interest, compound interest is an interest earned on the original investment AND on its accumulated interest. Compound interest is recommended for investing money (because it is a greater amount as it is interest on interest) but not for taking out a loan for the same reason, but this time you’d be paying more on your original loan.
Now, let’s use the given information to calculate how much money will Sipho receive from his investment after 2 years.
Investment period = 2 years
Number of times interest is compounded per year = 1 (the interest in compounded annually)
Accumulated amount after 1 year = principal amount + (principal amount x interest)
= 1000 + (1000 x 0.063)
= R 1063.00 (This value becomes the new principal amount.)
Accumulated amount after 2 years = 1063 + (1063 x 0.063)
= R 1129.97
At the end of his investment period, Sipho will have R1129,97. So, he would have earned R129.97 in interest on his original investment of R1000.
But, what if he wanted to invest it for a period of 7 or 10 years? It will be pen-ink and time-consuming to get to the solution if we use this long method of calculation.
Therefore, rather use this general formula to solve compound interest problems:
Where:
A – is the accumulated amount
P – is the principal amount
i – Is the interest rate
N – is the number of times interest is compounded each YEAR
Nt – is the number of times interest is compounded over the TOTAL period
In the example above, the interest was compounded annually. But imagine if the interest was compounded monthly, i.e. each month there was a new principal amount on which to calculate interest. In this instance, the interest earned would be higher. Test it yourself using the general formula:
i.e.
P = 1000
i = 6.3% or 0.063
n = 12 (because the interest is compounded monthly so there are 12 times in a year in which the interest is compounded, one for each month)
nt = 24 (the number of times that interest is compounded during the total period – as it is compounded monthly and as the investment is over a two year period, there are 24 periods for which it is compounded)
= 1000 (1 + 0.063/12)24
= R1133.91
So, if interest were compounded monthly, rather than annually, Sipho would earn R1133.91 instead of the original R1129.97 (i.e. almost R4 more). It may not seem like a big difference in this instance but for longer periods and using different amounts of investments it can add up. When looking at investment options always check how frequently the interest is compounded so that you can work out what would be the best for you.
Tell us: Have you tried this out? Does it make sense to you? Let us know!