IAI Actuarial Core Principles · Actuarial Mathematics for Modelling · Practical applications of the equation of value (loans and APR)
A bank must disclose a loan's cost as an APR of 10% effective per annum. What is the equivalent nominal annual rate convertible monthly, to two decimal places?
The nominal rate convertible monthly is 9.57%. The monthly rate is 1.10^(1/12) - 1, about 0.7974%, and multiplying by twelve gives 9.57%. It is lower than the 10% effective rate because monthly compounding adds interest within the year.
- A9.09%
- B9.31%
- C9.57%Correct
- D9.65%
- 10.00%
Explanation
The monthly rate j satisfies (1+j)^12 = 1.10, so j = 1.10^(1/12) - 1 = 0.797414%. The nominal rate is 12j = 9.57%. The 9.65% option uses quarterly conversion, 4(1.1^0.25 - 1). The 9.09% option is the effective discount rate, 0.1/1.1. The 10.00% option ignores conversion.
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