IAI Actuarial Core Principles · Actuarial Mathematics for Modelling · Equation of value
A lender advances Rs 95,000 to a borrower, who must repay Rs 1,00,000 exactly six months later, with no other payments. What is the effective annual rate of interest on this loan, to two decimal places?
The effective annual rate is 10.80%. The money grows by a factor of 100/95 = 1.0526 over six months, and compounding that over a full year gives 1.0526 squared, which is 1.1080, an effective rate of 10.80%.
- A10.25%
- B10.53%
- C5.26%
- D10.80%Correct
- 10.00%
Explanation
The six-month growth factor is 100,000/95,000 = 1.0526316. Squaring it gives the annual factor 1.108033, so the effective annual rate is 10.80%. 10.53% is the simple annualised rate (2 × 5.26%), which ignores compounding. 10.25% wrongly uses 5% as the six-month rate, which is based on 100,000 rather than 95,000.
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