Question

A $12,000 loan is repaid by semiannual payments of $1500 each. Interest on the loan is 10% compounded semiannually. How long will it take to pay off the loan?

Select one:

a. 10 years

b. 10.4 years

c. 5 years

d. 21 years

e. 5.2 years

Answer 1

Given,

Loan amount = $12000

Semi annual payment = $1500

Interest rate = 10% or 0.10

Solution :-

Semi annual interest rate (r) = 0.10/2 = 0.05

Let semi annual periods be 'n'

Now,

Loan amount = semi annual payment/r x [1 - (1 + r)^-n]

$12000 = $1500/0.05 x [1 - (1 + 0.05)^-n]

$12000 x 0.05/$1500 = 1 - (1.05)^-n]

0.4 = 1 - (1.05)^-n

0.4 - 1 = -(1.05)^-n

-0.6 = -(1.05)^-n

0.6 = (1.05)^-n

Taking 'Log' both sides,

Log(0.6) = Log(1.05)^-n

Log(0.6) = -n.Log(1.05)

-0.51082562377 = -n(0.0487901642)

0.51082562377 = n(0.0487901642)

0.51082562377/0.0487901642 = n

10.4698484242 = n

Now,

Number of years = 10.4698484242/2 = 5.2 years

So, it will take 5.2 years to pay off the loan.