Remaining Loan Annuity

At a glance, the rest of a loan is easy to calculate if the remaining loan is previously known. But what if we want to calculate the remainder of a loan but the rest of the previous loan is unknown?

Formula of Remaining Loan Annuity

Information :
Sm = Remaining Loan at period m
Im = Residual interest at period m
i = percentage of interest per period

Example Question of Remaining Loan Annuity

A loan of $10,000,000 will be repaid with a monthly annuity system with an interest rate of 3%/month for 2.5 years and the annuity is $510,192.59. Please specify the remaining loan after repayment for 10 months!

Answer :
i = 3%/month = 0.03/month

Determine first interest first:
$10,000,000 x 0.03 = $300,000

So the first interest is $ 300,000

Determine the first installment:
$510,192.59 - $300,000 = $210,192,59

Determine the 11th installment with the installment formula:
a₁₁ = $210,192.59(1 + 0.03)^11-1
a₁₁ = $210,192.59(1,03)¹⁰
a₁₁ = $210,192.59 x 1.3439164
a₁₁ = $282,481.26

Determine the 11th interest:
I₁₁ = $510,192.59 - $282,481.26
I₁₁ = $227,711.33

So the rest of the loan after repayment for 10 months is 7,590,377.67.
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