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Question
Solve the following :
A man borrowed some money and paid back in 3 equal installments of ₹2,160 each. What amount did he borrow if the rate of interest was 20% per annum compounded annually? Also find the total interest charged. [(1.2)3 = 0.5787]
Solution
Given, C = ₹2,160, n = 3 years, r = 20% p.a.
∴ i = `"r"/(100) = (2)/(100)` = 0.2
Here, we have to find present value of annuity.
∴ P = `"C"/"i"[1 - (1 + "i")^-"n"]`
= `(2,160)/(0.2)[1 - (1 + 0.2)^-3]`
= 10,800[1 – (1.2)–3]
= 10,800[1 – 0.5787]
= 10,800[0.4213]
∴ P = ₹4,550
The man has paid 3 equal instalments of ₹2,160 each.
∴ Total paid value of instalments
= 3 x 2,160
= ₹6,480
Interest = Total paid value of instalments – Present Value
= 6,480 – 4,550
= ₹1,930.
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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`
