Question

Bob has $7938 in student loans to repay, starting a year from now. The loan interest rate is 5%. If he repays $1429 annually at the end of each year, how long will it be before the loan to paid off? Round to the nearest year.

Answer 1

Given,

Loan amount = $7938

Interest rate (r) = 5% or 0.05

Annual repayment (A) = $1429

Solution :-

Let number of years be 'n'

Now,

Loan amount = A/r x [1 - (1 + r)^-n]

$7938 = $1429/0.05 x [1 - (1 + 0.05)^-n]

$7938 x 0.05/$1429 = 1 - (1.05)^-n

0.27774667599 = 1 - (1.05)^-n

(1.05)^-n = 1 - 0.27774667599

(1.05)^-n = 0.72225332401

Taking 'Log' both sides,

Log(1.05)^-n = Log(0.72225332401)

-n.Log(1.05) = Log(0.72225332401)

-n(0.048790164169) = -0.32537933735

n = -0.32537933735/-0.048790164169

n = 7

The answer is 7 years.