Question

Abu Saud would like to give his son a sum of money in 4 years if he is successful in completing his study. His son plans to use the money to buy a car which will cost SAR 60,000.

a. What would be the amount he needs to give to his son now to reach the goal of buying the

car if the money is invested in an account with a return of 10% compounded annually? b. If Abu Saud invested SAR 40,000 in the account now but at 10% simple interest rate

annually. Can his son reach the goal of buying the car? You should explain you answer.

Answer 1

(a) We can calculate the amount which Abu Saud needs to give his son now by simply applying compound interest formula

Amount needed after 4 years = Principal ( 1+ r/100 )ⁿ

Putting the values given in the question,

60,000 = Principal ( 1 + 10/100 )⁴

60,000 = Principal ( 1.1 )⁴ ( since, (1.1)⁴ = 1.4641 )

   Principal = 60,000/ 1.4641 = 40,981 (round of up to one decimal)

So, Abu Saud needs to give SAR 40,981 to his son now to reach the goal of buying the car if the money invested in an account with a return of 10% compounded annually.

(b) No, Abu Saud's son will not reach his goal if SAR 40,000 is invested in the account which yields a 10% simple interest rate.

We can prove this by simply calculating the amount after 4 years at a simple interest rate.

Amount after 4 years yielding a return of 10% simple interest = Principal + Simple Interest

= Principal + ( Principal Interest rate Time ) /100

= 40,000 + ( 40,000 10 4 ) / 100 = SAR 56,000

So, it is clear from above calculation that Abu Saud will not be able to meet the goal if amount is invested in an account which gives him 10% return at a simple interest rate.