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Question
What is the present value of an annuity due of ₹ 1,500 for 16 years at 8% per annum? What is the present value of an annuity due of ₹ 1,500 for 16 years at 8% per annum? [(1.08)16 = 3.172]
Solution
Present value of annuity due, P = `("a" (1 + "i"))/"i" [1 - 1/(1 + "i")^"n"]`
Here a = 1500, n = 16, i = `8/100` = 0.08
P = `(1500 (1 + 0.08))/(8/100) [1 - 1/(1.08)^16]`
= `(1500 xx 100 (1.08))/8 [1 - 1/(1.08)^16]`
= `150000/8 [1.08 - 1.08/(1.08)^16]`
= `150000/8 [1.08 - 1/(1.08)^16]`
= `18750 [1.08 - 1/3.1721]` ......[∵ (1.08)16 = 3.1721]
= 18750 [1.08 – 0.31524]
= 18750 [0.7648]
= ₹ 14340
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