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प्रश्न
Solve the following :
A company decides to set aside a certain amount at the end of every year to create a sinking fund that should amount to ₹9,28,200 in 4 years at 10% p.a. Find the amount to be set aside every year. [(1.1)4 = 1.4641]
उत्तर
Given, A = ₹9,28,200, n = 4 years, r = 10% p.a, i = `"r"/(100) = (10)/(100)` = 0.1
Now, A = `"C"/"i"[(1 + "i")^"n" - 1]`
∴ 9,28,200 = `"C"/(0.1)[(1 + 0.1)^4 - 1]`
∴ 9,28,200 x 0.1 = C[(1.1)4 – 1]
∴ 92,820 = C[1.4641 – 1]
∴ 92,820 = C(0.4641)
∴ C = `(92,820)/(0.4641)`
∴ C = ₹2,00,000
∴ The amount to be set aside each year is ₹2,00,000.
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A 35-year old person takes a policy for ₹ 1,00,000 for a period of 20 years. The rate of premium is ₹ 76 and the average rate of bonus is ₹ 7 per thousand p.a. If he dies after paying 10 annual premiums, what amount will his nominee receive?
The future amount, A = ₹ 10,00,000
Period, n = 20, r = 5%, (1.025)20 = 1.675
A = `"C"/"I" [(1 + "i")^"n" - 1]`
I = `5/200` = `square` as interest is calculated semi-annually
A = 10,00,000 = `"C"/"I" [(1 + "i")^"n" - 1]`
10,00,000 = `"C"/0.025 [(1 + 0.025)^square - 1]`
= `"C"/0.025 [1.675 - 1]`
10,00,000 = `("C" xx 0.675)/0.025`
C = ₹ `square`
For an annuity due, C = ₹ 2000, rate = 16% p.a. compounded quarterly for 1 year
∴ Rate of interest per quarter = `square/4` = 4
⇒ r = 4%
⇒ i = `square/100 = 4/100` = 0.04
n = Number of quarters
= 4 × 1
= `square`
⇒ P' = `(C(1 + i))/i [1 - (1 + i)^-n]`
⇒ P' = `(square(1 + square))/0.04 [1 - (square + 0.04)^-square]`
= `(2000(square))/square [1 - (square)^-4]`
= 50,000`(square)`[1 – 0.8548]
= ₹ 7,550.40
