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Question
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]
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Solution
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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For annuity due,
C = ₹ 20,000, n = 3, I = 0.1, (1.1)–3 = 0.7513
Therefore, P = `square/0.1 xx [1 - (1 + 0.1)^square]`
= 2,00,000 [1 – 0.7513]
= ₹ `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
