Amortization - SS3 Mathematics Lesson Note

This is a method of paying off a debt by gradually making partial payments called installment payments until the debt (principal) plus the interest are paid completely. If \(P\) is the principal, \(i\) the interest rate per period and \(n\) the number of periods, then \(R\) the installment payments is given by:

\[R = \frac{Pi}{1 - \left( \frac{1}{1 + i} \right)^{n}}\]

Example 7 Adam got a \(N1,200,000\) housing loan at an annual interest rate of \(10\%\). If the loan is amortized for a \(25\ year\ term\), what is the monthly payments the man is expected to pay?

Solution

\[P = 1200000,\ i = \frac{0.1}{12} = 0.0083333,\ n = 25 \times 12 = 300\]

\[R = \frac{1200000(0.0083333)}{1 - \left( \frac{1}{1 + 0.0083333} \right)^{300}} = N10,625.60\]