Question

Suppose that a loan is being repaid with 20 annual payments with the first payment coming one year from now. The first 5 payments are for $250, the next 8 are $310 each, and the final 7 are $430 each. If the effective rate of interest is 6.3%, how much interest is in the 11th payment?

Answer = $ (3 decimal place)

Answer 1

First 5 payments = $250
Next 8 payments = $310
Final 7 payments = $430

Effective interest = 6.3%

Balance after 10^th payment = $310/1.063 + $310/1.063^2 + $310/1.063^3 + $430/1.063^4 + $430/1.063^5 + $430/1.063^6 + $430/1.063^7 + $430/1.063^8 + $430/1.063^9 + $430/1.063^10
Balance after 10^th payment = $310 * (1 - (1/1.063)^3) / 0.063 + ($430/1.063^3) * (1 - (1/1.063)^7) / 0.063
Balance after 10^th payment = $2,810.35

Interest in 11^th payment = $2,810.35 * 6.3%
Interest in 11^th payment = $177.052