Question

​(Loan

amortization​)

To buy a new house you must borrow

$ 140 comma 000$140,000.

To do this you take out a

$ 140 comma 000$140,000​,

3030​-year,

88

percent mortgage. Your mortgage​ payments, which are made at the end of each year​ (one payment each​ year), include both principal and

88

percent interest on the declining balance. How large will your annual payments​ be?

Answer 1

Annual Loan Payment

Loan Amount (P) = $140,000

Annual Interest Rate (r) = 8.00% per year

Loan Period (n) = 30 Years

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

= [$140,000 x {0.08 x (1 + 0.08)³⁰}] / [(1 + 0.08)³⁰ – 1]

= [$140,000 x {0.08 x 10.0626569}] / [10.0626569 – 1]

= [$140,000 x 0.8050126] / 9.0626569

= $112,701.76 / 9.0626569

= $12,435.84 per year

“Hence, the annual mortgage payment will be $12,435.84 per year”