Amount borrowed = $1,250,000
Annual interest rate = 4.38%
Monthly interest rate = 0.365%
Period = 30 years or 360 months
Calculation of monthly payment:
Let monthly payment be $x
$1,250,000 = $x/1.00365 + $x/1.00365^2 + …. +
$x/1.00365^360
$1,250,000 = $x * (1 - (1/1.00365)^360) / 0.00365
$1,250,000 = $x * 200.16806
$x = $6,244.75
Monthly payment = $6,244.75
Calculation of loan outstanding after 39th payment:
Loan outstanding = $6,244.75/1.00365 + $6,244.75/1.00365^2 + … +
$6,244.75/1.00365^321
Loan outstanding = $6,244.75 * (1 - (1/1.00365)^321) /
0.00365
Loan outstanding = $6,244.75 * 188.89948
Loan outstanding = $1,179,630.03
Calculation of loan outstanding after 40th payment:
Loan outstanding = $6,244.75/1.00365 + $6,244.75/1.00365^2 + … +
$6,244.75/1.00365^320
Loan outstanding = $6,244.75 * (1 - (1/1.00365)^320) /
0.00365
Loan outstanding = $6,244.75 * 188.58896
Loan outstanding = $1,177,690.91
Loan repaid in 40th payment = Loan outstanding after
39th payment - Loan outstanding after 40th
payment
Loan repaid in 40th payment = $1,179,630.03 -
$1,177,690.91
Loan repaid in 40th payment = $1,939.12
Interest paid = Monthly payment - Loan repaid
Interest paid = $6,244.75 - $1,939.12
Interest paid = $4,305.63
Interest paid in percent = Interest paid / Monthly payment
Interest paid in percent = $4,305.63 / $6,244.75
Interest paid in percent = 0.6895 or 68.95%
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