Question

A loan is being repaid by quarterly installments of $1500 at the end of each quarter...

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.

Homework Answers

Answer #1

We need to find the value in retrospective

Formula:

Bt = L (1+i)t - RSt

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

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