IAI Actuarial Core Principles · Actuarial Mathematics for Modelling · Practical applications of the equation of value (loans and APR)
A loan of Rs 100,000 is repaid by five level annual payments in arrear. The effective annual rate of interest is 8%. What is the annual payment, to two decimal places?
The payment is Rs 25,045.65. For arrear payments the loan equals payment times the five-year annuity-immediate factor at 8%, which is 3.99271, so dividing 100,000 by that factor gives the level annual instalment.
- ARs 21,600.00
- BRs 23,190.42
- CRs 25,045.65Correct
- DRs 28,000.00
- Rs 30,192.08
Explanation
Payment = 100,000 / a(5) at 8%. a(5) = (1 - 1.08^-5)/0.08 = 3.99271, so payment = 100,000/3.99271 = 25,045.65. Using the annuity-due factor would give 23,190.42, which is wrong because payments are in arrear. Using a(4) would give 30,192.08.
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