Question

A homeowner planning a kitchen remodeling can afford a $200 monthly payment. How much can the homeowner borrow for 3 years at 3%, compounded monthly, and still stay within the budget? (Round your answer to the nearest cent.)

Answer 1

Let the amount of the loan be $ L. The formula used to calculate the fixed monthly payment (P) required to fully amortize a loan of $ L over a term of n months at a monthly interest rate of r is P = L[r(1 + r)ⁿ]/[(1 + r)ⁿ - 1] or, L = P[(1 + r)ⁿ - 1] /r(1 + r)ⁿ .

Here, P = $ 200, n = 3*12 = 36 and r = 3/1200 = 0.0025.

Hence L = 200*[(1.0025)³⁶-1]/[0.0025*(1.0025)³⁶] = 200*0.094051401/(0.0025*1.094051401) = 18.81028015/0.002735128503 = $ 6877.29 ( on rounding off to the nearest cent).

Thus, the homeowner borrow a sum of $ 6877.29.