IAI Actuarial Core Principles · Actuarial Mathematics for Modelling · Present value and accumulated value of cashflow streams
Rohan will receive Rs 50,000 at the end of each year for 4 years from a fund that earns 6% per annum effective. What is the present value of these payments, to the nearest rupee?
The present value is about Rs 1,73,255. Four year-end payments of Rs 50,000 are discounted at 6% using the annuity-immediate factor of 3.4651. The annuity-due value of Rs 1,83,610 would apply only if payments were made at the start of each year.
- ARs 1,73,255Correct
- BRs 1,75,000
- CRs 1,83,610
- DRs 2,00,000
- Rs 1,64,200
Explanation
PV = 50,000 × a(4) at 6%. v = 0.943396, and 1 − v^4 = 1 − 0.792094 = 0.207906. Dividing by 0.06 gives 3.465106. Multiplying by 50,000 gives 1,73,255. The figure 1,83,610 is the annuity-due value, which wrongly treats payments as made at the start of each year.
Did you get it right without looking?
One question tells you little. A timed set on Present value and accumulated value of cashflow streams shows your real accuracy, how long you take and where you lose marks.
More Present value and accumulated value of cashflow streams questions
- Payments of Rs 1,000 at time 1 and Rs 2,000 at time 3 (in years) are to be replaced by a single payment at time 2. At 5% effective per annum…
- The force of interest at time t years is δ(t) = 0.02 + 0.004t. What is the accumulated value at time 5 of an investment of ₹10,000 made at t…
- An annuity pays Rs 2,000 at the end of each year in perpetuity. At what effective annual interest rate is its present value Rs 25,000?
- A debt of Rs 12,000 due at the end of year 3 is to be settled by paying Rs 5,000 now and a payment X at the end of year 2. At an effective a…
- An investor receives Rs 100 at the end of each month for 2 years. The interest rate is 12% per annum nominal, convertible monthly. What is t…
- The nominal rate of interest convertible quarterly is 8% per annum. What is the equivalent effective annual rate, to two decimal places?