Question

# John borrowed \$125,000 to buy a house. His loan cost was 11% and he promised to...

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

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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