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प्रश्न
An annuity immediate is to be paid for some years at 12% p.a. The present value of the annuity is ₹ 10,000 and the accumulated value is ₹ 20,000. Find the amount of each annuity payment
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उत्तर
Given, P = ₹ 10,000, r = 12% p.a., A = ₹ 20,000
∴ i = `"r"/(100) = (12)/(100)` = 0.12
Now, `(1)/"P" - (1)/"A" = "i"/"C"`
∴ `(1)/(10,000) - (1)/(20,000) = (0.12)/"C"`
∴ `(2 - 1)/(20,000) = (012)/"C"`
∴ `(1)/(20,000) = (0.12)/"C"`
∴ C = (0.12)(20,000)
∴ C = 2,400
∴ The amount of each annuity payment is ₹ 2,400.
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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
