IAI Actuarial Core Principles · Actuarial Mathematics for Modelling · Present value and accumulated value of cashflow streams
A bank quotes a nominal rate of interest of 8% per annum convertible quarterly. What is the equivalent constant force of interest per annum, to two decimal places?
The equivalent force of interest is 7.92% per annum. A quarterly rate of 2% gives an annual accumulation factor of 1.02^4, so δ = 4 ln(1.02) = 0.0792. The effective annual rate of 8.24% and the discount rate of 7.62% are different measures.
- A7.62%
- B7.70%
- C7.92%Correct
- D8.00%
- 8.24%
Explanation
The quarterly rate is 2%, so δ = 4 ln(1.02) = 4 × 0.0198026 = 0.07921, which is 7.92%. The figure 8.24% is the effective annual rate, not the force. The figure 7.62% is the effective annual discount rate.
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