Question

Assume a 30-yeear, $600,000, 6% mortgage with annual payments.

What is the outstanding mortgage balance after you have made 10 payments?

Answer 1

Annual Mortgage Payment

Loan Amount = $600,000

Interest Rate (r) = 6%

Number of Periods (n) = 30 Years

Annual Payment = [P x {r (1+r)ⁿ} ] / [( 1+r)ⁿ – 1]

= [$600,000 x {0.06 x (1 + 0.06)³⁰}] / [(1 + 0.06) – 1]

= [$600,000 x (0.06 x 5.743491)] / [5.743491 – 1]

= [$600,000 x 0.34460] / 4.743491

= $206,765.68 / 4.743491

= $43,589.35

Outstanding mortgage balance after 10 payments

Remaining Loan Balance after 10 years = [Amount Borrowed x (1 + r) n] – [Monthly Payment x {{(1 + r)n -1}/ r]

= [$600,000 x (1 + 0.06)¹⁰] – [$43,589.35 x {{(1 + 0.06)¹⁰ -1}/ 0.06]

= [$600,000 x 1.790847] - [$43,589.35 x {( 1.790847 – 1) / 0.06}]

= $10,74,508.62 - $ 5,74,542.28

= $4,99,966.33

“Therefore, the Outstanding mortgage balance after 10 payments would be $4,99,966.33”