Remaining Loan Annuity

At a glance, the ease of a loan is slow to calculate if the remaining loan is previously known. But what if nosotros desire to calculate the residuum of a loan simply the ease of the previous loan is unknown?

Formula of Remaining Loan Annuity

Information :
Sm = Remaining Loan at menstruum m
Im = Residual involvement at menstruum m
i = per centum of involvement per period

Example Question of Remaining Loan Annuity

Influenza A virus subtype H5N1 loan of $10,000,000 volition last repaid amongst a monthly annuity organization amongst an involvement charge per unit of measurement of 3%/month for 2.5 years as well as the annuity is $510,192.59. Please specify the remaining loan afterwards repayment for x months!

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

Determine stimulate down involvement first:
$10,000,000 x 0.03 = $300,000

So the stimulate down involvement is $ 300,000

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

Determine the 11th installment amongst 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 ease of the loan afterwards repayment for x months is 7,590,377.67.
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Referensi :

• To'Ali's mass math grouping accounting as well as sales