IAI Actuarial Core Principles · Actuarial Mathematics for Modelling · Equation of value
A loan of Rs 500,000 is repaid by five level annual instalments, the first due one year after the loan is made. The effective annual interest rate is 10%. How much capital is repaid in the second instalment?
The second instalment repays Rs 90,088.61 of capital. The level instalment is Rs 131,898.74, the first year's capital is 131,898.74 − 50,000 = 81,898.74, and capital repayments grow by the interest rate, so 81,898.74 × 1.1 gives the answer.
- ARs 41,810.13
- BRs 81,898.74
- CRs 90,088.61Correct
- DRs 100,000.00
- Rs 131,898.74
Explanation
Instalment = 500,000/a(5) at 10% = 500,000/3.790787 = Rs 131,898.74. Year 1 interest is 50,000, so capital repaid is 81,898.74. Capital repaid in year 2 is this amount × 1.1 = Rs 90,088.61. Rs 81,898.74 is the first instalment's capital, not the second's.
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