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,

B_{4} = L (1+i)^{4} - RS_{4}

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**

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
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Please show/explain your work, I'd like to learn how to do it
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Answer should be: $10,814.16

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Please solve by hand, I need to know how to complete the problem
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Help please :)

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