Question

A $280,000 loan is to be paid with equal annual payment over a 15 year period. The interest rate on the loan is 4.5%. What is the remaining balance on the loan after 4 years?

Group of answer choices

$26,071.87

$222,364.78

$104,287.48

$175,712.52

Answer 1

Given,

Loan amount = $280000

Period (n) = 15 years

Interest rate (r) = 4.5% or 0.045

Solution :-

Annual payment = (Loan amount x r) $\div$ [1 - (1 + r)^-n]

= ($280000 x 0.045) $\div$ [1 - (1 + 0.045)^-15]

= $12600 $\div$ [1 - (1.045)^-15]

= $12600 $\div$ [1 - 0.51672044232]

= $12600 $\div$ 0.48327955768

= $26071.8662723

After 4 years,

Remaining period (t) = 15 years - 4 years = 11 years

Remaining balance in the loan after 4 years

= Annual payment/r x [1 - (1 + r)^-t]

= $26071.8662723/0.045 x [1 - (1 + 0.045)^-11]

= $26071.8662723/0.045 x [1 - (1.045)^-11]

= $26071.8662723/0.045 x [1 - 0.61619873878]

= $26071.8662723/0.045 x 0.38380126122

= $222364.78