Question

1. Ruth is planning for her son’s university education to begin 17 years from now. She estimates the yearly tuition, textbooks and living allowances to be approximately GHC25,000 per year for a four year degree.

(a) How much would she have to deposit today at an interest rate of 8 percent for her son to be able to withdraw GHC25,000 per year for four years?

(b) If Ruth decided to put an equal amount in a fixed deposit account at the end of every year, how much would she deposit every year at the same interest rate?           

2. One of your customers is delinquent on his accounts payable balance. You’ve mutually agreed to a repayment schedule of $300 per month. You will charge 1.5 percent per month interest on the overdue balance. If the current balance is $12,054.24, how long will it take for the account to be paid off?

Answer 1

1 .a ) The value of tuition fees at Year 17 beginning = 25000 + 25000/(1+8%) + 25000/(1+8%)³ + 25000/(1+8%)⁴
= 89427.42
PV of Investment = 89427.42/1.08¹⁷ = 24169.46

b) N=16 years for annuity
FV = Annuity at end of year *((1+r)ⁿ -1)/r
89427.42 = Annuity * ((1+8%)¹⁶-1)/8%
Annuity = 2949.04

2. rate of interest(r) = 1.5%/month
PV = 12054.24
PMT = 300
PV = Annuity * ( 1 -(1+r)^-n)/r
12054.24 = 300 * ( 1- ( 1+1.5%)^-n)/1.5%
12054.24*1.5%/300 = 1 -(1.015)^-n
0,602712 = 1 - (1.015)^-n
(1.015^-n) = 0.397288
-nLog1.015 = log(0.397288)
n = 61.99 or 62 months

Please discuss in case of doubts