Please help with Intrerest problem

Question

John needs money in 15 years’ time to pay for his son’s university fees. He is considering

three investments options:

(i) A single amount of $13250.with interest compounded continuously

(ii) 150 at the end of each month.

(iii) N$ 1750 at the beginning of each year.

a) If the interest rate is 10.5% p.a., how much will he get for each option?

b) What is the interest component for each investment?

Answer 1

Option (i), compound interest continuously is his best option for the maximum return.

(i) FV = PV x e ^{(i x t)}

FV = (13,250) * (2.78)^(0.105*15)

FV = $66,311

(ii) FV = 150 * (12*15)

FV = $27,000

Total = 27,000 + 13250 (his principal)

Total = $40,250

(iii) FV = 1750 * 15

FV = $26,250

Total = $27,000 + 13,250 (his principal)

Total = $39,500

Factor this into a 529 savings plan medium, and John's kid can enjoy these earnings dollar for dollar, without having tax consequences so long as these are used for educational purposes.