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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
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.
संबंधित 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]
Find the amount accumulated after 2 years if a sum of ₹ 24,000 is invested every six months at 12% p.a. compounded half yearly. [Given (1.06)4 = 1.2625]
Choose the correct alternative :
Amount of money today which is equal to series of payments in future is called
In an ordinary annuity, payments or receipts occur at ______.
Choose the correct alternative :
Rental payment for an apartment is an example of
Fill in the blank :
The intervening time between payment of two successive installments is called as ___________.
Fill in the blank :
If payments of an annuity fall due at the beginning of every period, the series is called annuity __________.
State whether the following is True or False :
Payment of every annuity is called an installment.
State whether the following is True or False :
Annuity contingent begins and ends on certain fixed dates.
State whether the following is True or False :
Sinking fund is set aside at the beginning of a business.
Solve the following :
Find the rate of interest compounded annually if an ordinary annuity of ₹20,000 per year amounts to ₹41,000 in 2 years.
Solve the following :
A person purchases a television by paying ₹20,000 in cash and promising to pay ₹1,000 at end of every month for the next 2 years. If money is worth 12% p. a. converted monthly, find the cash price of the television. [(1.01)–24 = 0.7875]
Multiple choice questions:
Rental payment for an apartment is an example of ______
State whether the following statement is True or False:
The relation between accumulated value ‘A’ and present value ‘P’ is A = P(1+ i)n
In ordinary annuity, payments or receipts occur at ______
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`
The future amount, A = ₹ 10,00,000
Period, n = 20, r = 5%, (1.025)20 = 1.675
A = `"C"/"I" [(1 + "i")^"n" - 1]`
I = `5/200` = `square` as interest is calculated semi-annually
A = 10,00,000 = `"C"/"I" [(1 + "i")^"n" - 1]`
10,00,000 = `"C"/0.025 [(1 + 0.025)^square - 1]`
= `"C"/0.025 [1.675 - 1]`
10,00,000 = `("C" xx 0.675)/0.025`
C = ₹ `square`
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
