IAI Actuarial Core Principles · Actuarial Mathematics for Modelling · Equation of value
A bank lends Rs 5,00,000 to be repaid by five equal annual instalments, the first paid one year after the loan is made. Interest is charged at 8% effective per annum. What is the annual instalment?
The instalment is Rs 125,228.23. The loan equals the present value of five equal year-end payments, so the payment is 5,00,000 divided by the five-year annuity-immediate factor at 8%, which is 3.992710.
- ARs 125,228.23Correct
- BRs 100,000.00
- CRs 115,952.06
- DRs 140,000.00
- Rs 146,932.81
Explanation
Payment = 500,000 / a(5) at 8%. a(5) = (1 − 1.08^-5)/0.08 = 3.992710, giving 125,228.23. Rs 115,952.06 treats the payments as annuity-due, which is wrong because the first payment is at the end of year 1. Rs 146,932.81 is the accumulated loan divided by 5.
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