Question

A loan is made for $175,000 at 10% for 25 years. Payments are made monthly and the loan is fully amortizing. What will the balance be at the end of 8 years?

136,310.71

173,913.56

147,933.76

155,719.74

Answer 1

Monthly Loan Payment

Loan Amount (P) = $175,000

Monthly Interest Rate (n) = 0.833333% per month [10.00% / 12 Months]

Number of months (n) = 300 Months [25 Years x 12 Months]

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

= [$175,000 x {0.00833333 x (1 + 0.00833333)³⁰⁰}] / [(1 + 0.00833333)³⁰⁰ – 1]

= [$175,000 x {0.00833333 x 12.0569450}] / [12.0569450 – 1]

= [$175,000 x 0.1004745] / 11.0569450

= $17,583.04 / 11.0569450

= $1,590.23 per month

Outstanding balance of the loan at the end of 8^th year

The outstanding principal after 5 years is calculated by using the following formula

Remaining Balance = [Amount Borrowed x (1 + r) ⁿ] – [Annual Payment x {{(1 + r)ⁿ -1}/ r]

Here, we’ve Loan Amount (P) = $175,000

Monthly Interest Rate (n) = 0.833333% per month [10.00% / 12 Months]

Number of months (n) = 96 Months [8 Years x 12 Months]

Monthly loan payment = $1,590.23 per year

Therefore, the Outstanding balance of the loan at the end of 8th year = [Amount Borrowed x (1 + r) ⁿ] – [Monthly Payment x {{(1 + r)ⁿ -1}/ r]

= [$175,000 x (1 + 0.00833333)⁹⁶] – [$1,590.23 x {{(1 + 0.00833333)⁹⁶ -1}/ 0.00833333]

= [$175,000 x 2.2181756] – [$1,590.23 x {(2.2181756 - 1) / 0.00833333]

= [$175,000 x 2.2181756] – [$1,590.23 x {1.2181756 / 0.00833333}]

= [$175,000 x 2.2181756] – [$1,590.23 x 146.1810757]

= $388,180.74 - $232,461.00

= $155,719.74

“Hence, the Outstanding balance of the loan at the end of 8th year will be $155,719.74”