IAI Actuarial Core Principles · Actuarial Mathematics for Modelling · Time value of money: compound interest and discounting
Rohit invests ₹16,000 for 2 years in an account where the effective annual rate of discount is 20%. What is the accumulated value at the end of 2 years?
The accumulated value is ₹25,000. With an effective discount rate of 20%, money grows by a factor of 1/0.8, which is 1.25, each year. Over two years the factor is 1.5625, and 16,000 multiplied by 1.5625 gives ₹25,000.
- A₹23,040.00
- B₹26,666.67
- C₹20,000.00
- D₹10,240.00
- ₹25,000.00Correct
Explanation
The accumulation factor per year is 1/(1−d) = 1/0.8 = 1.25. Over 2 years the accumulated value is 16,000 × 1.25^2 = 16,000/0.64 = ₹25,000. ₹23,040 wrongly uses 1.2^2, and ₹26,666.67 wrongly uses simple discount 1−2d = 0.6.
Did you get it right without looking?
One question tells you little. A timed set on Time value of money: compound interest and discounting shows your real accuracy, how long you take and where you lose marks.
More Time value of money: compound interest and discounting questions
- A zero-coupon bond pays Rs 1,00,000 at the end of 5 years. It is priced at Rs 74,726 today. What effective annual rate of interest does this…
- A sum of money doubles under simple interest at 8% per annum and, separately, under compound interest at 8% per annum effective. By how many…
- An investor is due to receive Rs 50,000 in 4 years' time. The effective annual rate of interest is 6%. What is the present value of this pay…
- Rajesh invests Rs 50,000 for 3 years at 8% per annum simple interest. Priya invests Rs 50,000 for the same period at 8% per annum effective …
- The force of interest is a constant 6% per annum. A sum of Rs 50,000 is due in 5 years. What is its present value to the nearest rupee?
- The force of interest is a constant 5% per annum. What is the present value of Rs 100,000 payable in 3 years, to the nearest rupee?