R1000 is invested for 2 years at a compound interest rate of 7% p.a. Calculate the compound interest earned after 2 years.

Steps to Solve

1. Write down the compound interest formula

The formula for compound interest is:

$A = P(1 + \frac{r}{n})^{nt}$

Where: $A$ = the future value of the investment/loan, including interest $P$ = the principal investment amount (the initial deposit or loan amount) $r$ = the annual interest rate (as a decimal) $n$ = the number of times that interest iscompounded per year $t$ = the number of years the money is invested or borrowed for

2. Identify the values for each variable

From the problem statement: $P = R1000$ $r = 7% = 0.07$ $n = 1$ (since the interest is compounded annually) $t = 2$ years

3. Substitute the values into the formula

Substitute the values of $P$, $r$, $n$, and $t$ into the compound interest formula:

$A = 1000(1 + \frac{0.07}{1})^{(1)(2)}$

4. Calculate the value of A

Simplify the equation:

$A = 1000(1 + 0.07)^2$ $A = 1000(1.07)^2$ $A = 1000(1.1449)$ $A = 1144.90$

So, the future value of the investment after 2 years is R1144.90.

5. Calculate the compound interest earned

To find the compound interest earned, subtract the principal amount from the future value:

$Compound\ Interest = A - P$ $Compound\ Interest = 1144.90 - 1000$ $Compound\ Interest = 144.90$

Therefore, the compound interest earned is R144.90.