Question

A loan is being repaid by quarterly installments of $1500 at the end of each quarter at 10% convertible quarterly. If the loan balance at the end of the first year is $12,000. Find the original loan balance.

Answer 1

We need to find the value in retrospective

Formula:

B_t = L (1+i)^t - RS_t

We have completed the 4 quarter. So,

B₄ = L (1+i)⁴ - RS₄

B = Outstanding principal at the end of four quarters

L = ?

i = 10%/4 = 2.5%

R = Quaterly payment

S = ((1+i)⁴-1)/i

12,000 = L(1+0.025)⁴ - 1500*((1+0.025)⁴-1)/0.025

12000 = L(1.025)⁴ - 1500*((1.025)⁴-1)/0.025

12000 = L(1.025)⁴ - 6228.77

L(1.025)⁴ = 18228.77

L = 18228.77/(1.025)⁴

L = $16,514.37

Original loan balance = $16,514.37