IAI Actuarial Core Principles · Actuarial Mathematics for Modelling · Equation of value
An investor puts Rs 10,000 into a deposit and receives a single payment of Rs 12,100 exactly two years later, with no other cashflows. What is the effective annual rate of interest earned?
The effective annual rate is 10.00%. The accumulation factor over two years is 12,100/10,000 = 1.21, and taking the square root gives an annual factor of 1.10. Dividing the 21% total gain by two would ignore compounding.
- A9.53%
- B10.00%Correct
- C10.50%
- D11.00%
- 21.00%
Explanation
Solve 10,000(1+i)^2 = 12,100, so (1+i)^2 = 1.21 and 1+i = 1.10, giving i = 10%. 10.50% is wrong because it divides the total 21% gain by 2, which ignores compounding. 9.53% is the equivalent force of interest, not the effective rate.
Did you get it right without looking?
One question tells you little. A timed set on Equation of value shows your real accuracy, how long you take and where you lose marks.
More Equation of value questions
- A bank lends Rs 5,00,000 to be repaid by five equal annual instalments, the first paid one year after the loan is made. Interest is charged …
- An annuity pays Rs 1,000 at the end of year 1, Rs 2,000 at the end of year 2 and Rs 3,000 at the end of year 3. The effective annual interes…
- A lender quotes a nominal rate of discount of 8% per annum convertible quarterly. What is the equivalent effective annual rate of interest, …
- The nominal rate of interest is 12% per annum convertible quarterly. What is the equivalent effective annual discount rate, to 4 decimal pla…
- A payment of Rs 1,00,000 is due in 4 years. The force of interest is constant at 6% per annum. What is its present value, to two decimal pla…
- Rs 1,000 is invested at the end of each of the next 3 years in an account that credits interest at a nominal rate of 8% per annum convertibl…