The Size of the Monthly Repayment $k$ That Amortizes a Loan Of

question 14

Short Answer

The size of the monthly repayment $k$ that amortizes a loan of $A$ dollars in $N$ years at an interest rate of $r$ per year, compounded monthly, on the unpaid balance is given by
$$k = \frac { A r } { 12 \left[ 1 - \left( 1 + \frac { r } { 12 } \right) ^ { - 12 N } \right] }$$
The value of $r$ can be found by performing the iteration
$$r _ { n + 1 } = r _ { n } - \frac { A r _ { n } + 12 k \left[ \left( 1 + \frac { r _ { n } } { 12 } \right) ^ { - 12 N } - 1 \right] } { A - 12 N k \left( 1 + \frac { r _ { n } } { 12 } \right) ^ { - 12 N - 1 } }$$
A family secured a loan of $\$ 360,000$ from a bank to finance the purchase of a house. They have agreed to repay the loan in equal monthly installments of \$2476 over 25 years. Find the interest rate on this loan. Round the rate to one decimal place.

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