IAI Actuarial Core Principles · Actuarial Mathematics for Modelling · Annuity and accumulation functions
An investor deposits Rs 50,000 in an account where the accumulation function is A(t) = 1 + 0.06t for 0 ≤ t ≤ 10 (simple interest). What is the effective annual rate of interest in the fifth year (from t = 4 to t = 5)?
The effective rate in the fifth year is 4.84%. Under simple interest the accumulation grows from 1.24 at time 4 to 1.30 at time 5, an increase of 0.06, and the rate is measured against the opening value 1.24, giving 0.06/1.24.
- A6.00%
- B5.00%
- C4.84%Correct
- D4.55%
- 4.76%
Explanation
A(4) = 1.24 and A(5) = 1.30. The effective rate in year 5 is (A(5) - A(4))/A(4) = 0.06/1.24 = 4.84%. Using 0.06 divided by A(5) = 1.30 gives 4.62%, which is the wrong base. Option 6.00% ignores that simple interest produces a falling effective rate.
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