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प्रश्न
A person invested ₹ 5,000 every year in finance company that offered him interest compounded at 10% p.a., what is the amount accumulated after 4 years? [Given (1.1)4 = 1.4641]
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उत्तर
Given, C = ₹ 5,000, r = 10%p.a., n = 4 years
i = `"r"/100 = 10/100` = 0.1
It is an immediate annuity.
Now, A = `"C"/"i"[(1 + "i")^"n" - 1]`
= `(5,000)/(0.1)[1 + 0.1^4 - 1]`
= 50,000[(1.1)4 – 1]
= 50,000[1.4641 – 1]
= 50,000(0.4641)
= 23,205
∴ Amount accumulated after 4 years is ₹ 23,205.
संबंधित प्रश्न
Find accumulated value after 1 year of an annuity immediate in which ₹ 10,000 is invested every quarter at 16% p.a. compounded quarterly. [Given (1.04)4 = 1.1699]
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State whether the following is True or False :
The present value of an annuity is the sum of the present value of all installments.
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A shopkeeper insures his shop and godown valued at ₹5,00,000 and ₹10,00,000 respectively for 80 % of their values. If the rate of premium is 8 %, find the total annual premium.
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Solve the following :
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Solve the following :
Some machinery is expected to cost 25% more over its present cost of ₹6,96,000 after 20 years. The scrap value of the machinery will realize ₹1,50,000. What amount should be set aside at the end of every year at 5% p.a. compound interest for 20 years to replace the machinery? [Given (1.05)20= 2.653]
Multiple choice questions:
In annuity calculations, the interest is usually taken as ______
Multiple choice questions:
If for an immediate annuity r = 10% p.a., P = ₹ 12,679.46 and A = ₹ 18,564, then the amount of each annuity paid is ______
State whether the following statement is True or False:
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State whether the following statement is True or False:
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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
