IAI Actuarial Core Principles · Actuarial Mathematics for Modelling · Equation of value
A deposit of Rs 40,000 accumulates to Rs 46,866.38 after exactly two years under a fixed rate of interest. What is the nominal annual rate of interest convertible quarterly?
The nominal rate convertible quarterly is 8.00%. The two-year growth factor of 1.171659 equals (1+j) to the power 8, giving a quarterly rate j of 2%, and multiplying by four gives 8%. The effective annual rate would be a different figure, 8.24%.
- A2.00%
- B7.92%
- C8.00%Correct
- D8.24%
- 8.58%
Explanation
Accumulation factor = 46,866.38/40,000 = 1.171659 = (1 + j)^8, so 1 + j = 1.02 and j = 2% per quarter. The nominal rate convertible quarterly is 4 x 2% = 8%. 8.24% is the effective annual rate (1.02^4 - 1), and 2.00% is the quarterly rate itself.
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
- An investor pays Rs 10,00,000 now and receives Rs 5,50,000 at the end of year 1 and Rs 6,05,000 at the end of year 2. What is the internal r…
- Rs 2,000 is deposited at the start of each year for 10 years into an account earning 7% effective annual interest. What is the accumulated v…
- A sum of Rs 20,000 is invested for 3 years at a nominal rate of 12% per annum convertible monthly. What is the accumulated value, to two dec…
- An investment requires an outlay of Rs 1,000 now and pays Rs 600 at the end of year 1 and Rs 600 at the end of year 2. What is the yield (in…
- A project requires an outlay of Rs 10,000 now and returns Rs 5,500 at the end of year 1 and Rs 6,050 at the end of year 2. What is the yield…
- An annuity-immediate pays Rs 1,000 at the end of each year for 5 years. Using an effective annual interest rate of 8%, what is its present v…