Question

(1 point) A 25-year loan is to be repaid with equal installments at the end of each yeas. The amount of interest paid in the 6th installment is $156. The amount of interest paid in the 16th installment is $126. Calculate the amount of interest paid in the 21st installment ANSWER-$

Answer 1

Let K be the amount of annual Installment then the amount of Interest paid in Installment t is

I_t = K ( 1 - v ^n-t+1 ) , where n = 25

So given = I ₆= k ( 1 - v ²⁰ ) = 156

I ₁₆ = k ( 1 - v ¹⁰ ) = 126

I ₂₁ = k ( 1 - v ⁵ )

156/126 = 1 - v ²⁰ / 1 - v ¹⁰

( 1 - v ¹⁰ ) ( 1 + v ¹⁰ ) / ( 1 - v ¹⁰ ) = 156/126

v ¹⁰ = 156/126 -1

v ¹⁰ = 0.238

v ⁵ =

V0.238

v ⁵ = 0.49 = 0.5

therefore, K ( 1 - v ¹⁰) = 126

k ( 1 - 0.238 ) = 126

k = 126/0.762 = 165.35

I ₂₁ = K ( 1 - v ⁵ ) = 165.35 ( 1 - 0.5 ) = 165.35 * 0.5 = $82.675

ANSWER - $82.675