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For an annuity due, C = ₹ 2000, rate = 16% p.a. compounded quarterly for 1 year ∴ Rate of interest per quarter = □4 = 4 ⇒ r = 4% ⇒ i = □100=4100 = 0.04 n = Number of quarters = 4 × 1 = □ - Mathematics and Statistics

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Question

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

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Solution

For an annuity due, C = ₹ 2000, rate = 16% p.a. compounded quarterly for 1 year

∴ Rate of interest per quarter = `bb(16)/4` = 4

⇒ r = 4%

⇒ i = `bbr/100 = 4/100` = 0.04

n = Number of quarters

= 4 × 1

= 4

⇒ P' = `(C(1 + i))/i [1 - (1 + i)^-n]`

⇒ P' = `(bb(2000)(1 + bb(0.04)))/0.04 [1 - (bb(1) + 0.04)^-bb(4)]`

= `(2000(bb(1.04)))/bb(0.04) [1 - (bb(1.04))^-4]`

= 50,000(1.04)[1 – 0.8548]

= 50,000(1.04)(0.1452)

= ₹ 7,550.40

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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`


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