Question

Bob Smith borrowed $200,000 on January 1, 2015. The interest rate of 8% is compounded semiannually to be repaid January 1, 2025. To repay this Bob wants to start making five equal annual deposits into fund that earns 6% annum on January 1, 2020.

Required:What is the amount of the five annual deposits that Bob needs to make?

Answer 1

Solution:

Given data,

Present value = $200,000

Interest rate = 8% and

Earns 6% annum on january 1, 2020

From the given data we need to find the given requirement,

FV of the loan is = PV * (1+i)^n

PV = $200,000

i = 4% (8%/2)

n= 2*10 = 20

= $200,000 (1+0.04)^20

Future value (FV) = $438,225

So he need to pay $438,225 on 1 jan 2025.

we need to calculate the annual deposit by future value of annuity

FV = C * ((1+i)^n-1)/i

i = 6%

n=10

$438,225 = C * ((1+6%)^10-1)/6%

$438,225 = C * 13.18

C= $33,249

The amount of five annual deposits that Bob needs to make: C = $33,249