Question

Kirby takes out a $1,000 loan that is to be repaid with equal payments at the end of each year for 20 years. the principal portion of the 12th payment is 1.5 times the principal portion of the 4th payment.

a) What is the interst rate on the loan?

b) How much are the payments on the loan?

Answer 1

a) Using trial and error, we can calculate the interest rate.

Principal paid in a payment can be calculated using CUMPRINC function

At 5.2% rate, we get principal paid in 12th payment

CUMPRINC(rate = 5.2%, nper = 20, pv = 1000, 12, 12, 0) = $51.71

and Principal paid in 4th payment

CUMPRINC(rate = 5.2%, nper = 20, pv = 1000, 4, 4, 0) = $34.47

Hence, at 5.2%, principal paid in 12th payment is 1.5 times that paid in 4th payment.

b) Monthly payment can be calculated using PMT function

PMT = PMT(rate = 5.2%, nper = 20, pv = 1000, fv = 0, 0) = $81.61