Question

Nathan Drake is considering borrowing $100,000 for 30 years at a compound annual interest rate of 13.675% p.a. The loan agreement calls for 30 equal annual payments, to be paid at the end of each of the next 30 years (payments include both principal and interest.) What is the annual payment that will fully amortize Nathan’s loan?

Answer 1

The question involves calculating the annual payment needed for a $100,000 loan with a 13.675% compound annual interest over 30 years using the annuity formula.

Step-by-step explanation:

The student's question pertains to calculating the annual payment required to fully amortize a 30-year loan of $100,000 with a compound annual interest rate of 13.675%. To find the annual payment, we can use the annuity formula which accounts for the present value of annuity payments, the interest rate, and the number of payments. The formula takes the form:

PV = PMT * [1 - (1 + r)^-n] / r

Where PV is the present value (the loan amount), PMT is the annual payment, r is the annual interest rate (expressed as a decimal), and n is the number of payments (years in this case).

Rearranging the formula to solve for PMT gives:

PMT = PV / [1 - (1 + r)^-n] / r

By substituting the relevant values (PV = $100,000, r = 0.13675, n = 30) and solving for PMT, we will determine the annual payment that Nathan Drake needs to make to fully amotize his loan.