Question

Consider a loan for $72,675 that is paid off in 15 yearly payments of $6,000.

How to manipulate the formula to solve for Interest rate?

What is the interest rate?

Show your work?

Answer 1

Loan Amount = $72,625

n = 15 yearly payments

P = Yearly payment = $6,000

Loan Amount = P * [1 - (1+r)^-n] / r

$72,625 = $6,000 * [1 - (1+r)^15] / r

[1 - (1+r)^15] / r = 12.1041666667

Find present value of annuity factor from PVIFA table for 15 years

PVIFA (2%,15 years) = 12.8493

PVIFA (3%,15 years) = 11.9379

from the above factors, the interest rate is between 2% and 3%

fraction interest rate = (PVIFA @2% - Actual PVIFA ) / (PVIFA @2% - PVIFA @3%)

= (12.8493 - 12.1041666667) / (12.8493 - 11.9379)

= 0.745133333 / 0.9114

= 0.8175700384%

Interest rate = 2% + 0.8175700384% = 2.8175700384% = 2.82%

Therefore, interest rate is 2.82 %