Question

Your grandparents gave you a gift of R2 000 on your 16th birth day. You want to invest the money in an account over four years. You have an option of investing the R2 000 at 8% per annum simple interest or 8% per annum compound interest.Determine,through calculations, which investment will be more profitable.

Answer 1

Task. Your grandparents gave you a gift of 2000 on your 16th birth day. You want to invest the money in an account over four years. You have an option of investing the 2000 at 8% per annum simple interest or 8% per annum compound interest. Determine, through calculations, which investment will be more profitable.

Solution. Let $P=2000$ be the initial amount of money (principal), $r=0.08$ the interest rate, and $n=4$ number of years. Then the amount of money in $n$ years with simple interest per annum at rate $r$ is given by the formula:

$A_{1}=P(1+rn)=2000*(1+0.08*4)=2640.$

On the other hand, compound interest with the same $P$, $r$ and $n$ is equal to

$A_{2}=A(1+r)^{n}=2000*(1+0.08)^{4}\approx 2721.0>A_{1}=2640.$

Hence the investment with compound interest per annum is more profitable.

Answer. The investment with compound interest per annum is more profitable.