IAI Actuarial Core Principles · Actuarial Mathematics for Modelling · Present value and accumulated value of cashflow streams
A loan of Rs 1,00,000 is repaid by two payments: Rs 60,000 at the end of year 1 and Rs X at the end of year 2. The effective annual rate of interest is 10%. What is X, to the nearest rupee?
X equals Rs 55,000, found from the equation of value 100,000 = 60,000/1.1 + X/1.21. The balance after year 1 is 50,000, which accumulates to 55,000 at 10%.
- ARs 40,000
- BRs 44,000
- CRs 49,000Correct
- DRs 50,000
- Rs 53,000
Explanation
Equation of value at time 0: 100,000 = 60,000/1.1 + X/1.21. 60,000/1.1 = 54,545.45, leaving 45,454.55. Multiplying by 1.21 gives X = 55,000. Check: outstanding after year 1 is 110,000 − 60,000 = 50,000, which grows to 55,000. So the key must be 55,000, which is not among the options.
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
- 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…
- A nominal rate of 12% per annum convertible monthly is equivalent to a force of interest closest to which value?
- 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?
- The force of interest is a constant 6% per annum. Money is paid continuously at a constant rate of ₹1,000 per annum for 5 years into an acco…
- Rohan invests Rs 50,000 in a deposit earning 8% per annum effective. What is the accumulated value at the end of 3 years?