Question

A bank makes a loan of 20,000 at an interest rate of i.

The loan will be repaid with level payments at the end of each year for 20 years.

When the bank receives each payment, it reinvests at a rate of 5%.

At the end of the 20 year period, the bank calculates the annual effective return over the loan period to be 6.5%.

What is i, the original interest rate on the loan?

Answer 1

Future value = present value*(1+r)^n

r = effective annual rate = 6.5%

n = number of periods

Present value = loan amount = 20,000

So Future value after 20 years = 20000*(1+5%)^20

= $70,472.90

Using financial calculator:

We know,

N = 20 years

PMT = ? ( reinvestment amounts)

I/Y = 5%

FV = 70,472.90

PV = 0

[N = 20 ; I/Y = 5% ; PV = 0 ; PMT = ? ; FV = 70472.90]

Compute PMT

Annual reinvestment amounts = $2131.28

Above amount is the yearly payments of original loan of 20,000

Using above figures now we can calculate i

[N = 20 ; I/Y = ? ; PV = 20000 ; PMT = 2131.28 ; FV = 0]

Compute for I/Y

So original interest rate (i) = 8.62%