Answer: 10 years, 175 days
Explanation:
Given the following ;
Payment per period(PMT) = $4000
PERIOD(n) = 4 years
Interest(r) = 12% = 0.12 per annum
Firstly,
Calculating the present value(PV) of the payment per period at 12% rate for 4 years
PV = [PMT(1 - (1 + r) ^-n)] ÷ r
PV = [4000 (1 - (1 + 0.12)^-4)] ÷ 0.12
PV = [4000 ( 1 - (1.12)^-4)] ÷ 0.12
PV = [4000 ( 1 - 0.635518078)] ÷ 0.12
PV = $12,149 (to the nearest whole number)
Now we calculate the period ;
if a deposit of $2542 is made
PV = [P(1 - (1 + r) ^-n)] ÷ r
12149 = [2542(1 - (1.12)^-n)]÷ 0.12
1457.88 = 2542.05(1 - (1.12)^-n)
2542 - 2542(-1.12^-n) = 12149 ×1.12
Log0.42648 = - n * log1.12
n = 7.52 years
There for payment will be made for 7.52 years
Present age = 18 - 7.52 = 10.48
10.48years.
10years, 175 days
