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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Definitions:

Training Costs

The expenses incurred in the development and delivery of training programs for employees, aimed at enhancing their skills, knowledge, and performance.

Psychological Factors

Elements of human psychology that influence behavior, thinking, and emotional state.

Learning Principle

A foundational concept in educational psychology that explains how individuals acquire new knowledge or skills through various methods of learning.

Commitment

The dedication or loyalty of an individual or group to a cause, activity, organization, or relationship, often manifesting as continued involvement and effort.