Question

John borrowed $125,000 to buy a house. His loan cost was 11% and he promised to repay the loan in 15 equal annual payments. How much principal is amortized with the first payment?

$17, 383

$13,750

$3,633

$121,367

Answer #1

PV = Loan amount = $125,000

n = 15 annual payments

r = interest rate = 11%

Annual loan payment = [r * PV] / [1 - (1+r)^-n]

= [11% * $125,000] / [1 - (1+11%)^-15]

$13,750 / 0.79099565335

= $17,383.1549412

Annual loan payment = $17,383

Interest on loan for the first year = $125,000 * 11% = $13,750

Principal amortized for first year = Annual loan payment - Interest on loan for the first year

= $17,383 - $13,750

= $3,633

Therefore, Principal amount amortized with first payment is $3,633

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