Question

Find the monthly payment needed to amortize a typical $205,000 mortgage loan amortized over 30 years at an annual interest rate of 7.1% compounded monthly. (Round your answers to the nearest cent.) a) $ b) Find the total interest paid on the loan. $

Answer 1

(a)-Monthly Loan Payment

Here, we’ve Loan Amount (P) = $205,000

Monthly Interest Rate (n) = 0.591667% per month [7.10% / 12 Months]

Number of months (n) = 360 Months [30 Years x 12 Months]

Therefore, the Monthly Loan Payment = [P x {r (1 + r)ⁿ} ] / [(1 + r)ⁿ – 1]

= [$205,000 x {0.00591667 x (1 + 0.00591667)³⁶⁰}] / [(1 + 0.00591667)³⁶⁰ – 1]

= [$205,000 x {0.00591667 x 8.3622163}] / [8.3622163 – 1]

= [$205,000 x 0.0494764] / 7.3622163

= $10,142.67 / 7.3622163

= $1,377.67 per month

(b)-Total interest paid on the loan

Total interest paid on the loan = Total Loan Payment – Loan Amount

= [$1,377.67 per month x 360 Months] - $205,000

= $495,961.20 - $205,000

= $290,961.20