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प्रश्न
A lady plans to save for her daughter’s marriage. She wishes to accumulate a sum of ₹ 4,64,100 at the end of 4 years. What amount should she invest every year if she gets an interest of 10% p.a. compounded annually? [Given (1.1)4 = 1.4641]
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उत्तर
Given: A = ₹ 4,64,100, n = 4 years, r = 10% p.a.
i = `r/(100) = (10)/(100)` = 0.1
Now, A = `C/i[(1 + i)^n - 1]`
∴ 4,64,100 = `C/(0.1)[(1 + 0.1)^4 - 1]`
∴ 4,64,100 × (0.1) = C[(1.1)4 – 1]
∴ 46,410 = C[1.4641 – 1]
∴ 46,410 = C(0.4641)
∴ C = `(46,410)/(0.4641)`
∴ C = 1,00,000
∴ She must invest ₹ 1,00,000 every year.
संबंधित प्रश्न
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]
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]
A person wants to create a fund of ₹ 6,96,150 after 4 years at the time of his retirement. He decides to invest a fixed amount at the end of every year in a bank that offers him interest of 10% p.a. compounded annually. What amount should he invest every year? [Given (1.1)4 = 1.4641]
Find the accumulated value of annuity due of ₹1,000 p.a. for 3 years at 10% p.a. compounded annually. [Given (1.1)3 = 1.331]
For an annuity immediate paid for 3 years with interest compounded at 10% p.a., the present value is ₹24,000. What will be the accumulated value after 3 years? [Given (1.1)3 = 1.331]
Choose the correct alternative :
You get payments of ₹8,000 at the beginning of each year for five years at 6%, what is the value of this annuity?
In an ordinary annuity, payments or receipts occur at ______.
______ is a series of constant cash flows over a limited period of time.
Fill in the blank :
The payment of each single annuity is called __________.
Fill in the blank :
An annuity where payments continue forever is called __________.
State whether the following is True or False :
Payment of every annuity is called an installment.
State whether the following is True or False :
Sinking fund is set aside at the beginning of a business.
Solve the following :
Find the amount of an ordinary annuity if a payment of ₹500 is made at the end of every quarter for 5 years at the rate of 12% per annum compounded quarterly. [(1.03)20 = 1.8061]
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.
Multiple choice questions:
In an ordinary annuity, payments or receipts occur at ______
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:
The future value of an annuity is the accumulated values of all instalments
State whether the following statement is True or False:
Annuity contingent begins and ends on certain fixed dates
State whether the following statement is True or False:
An annuity where payments continue forever is called perpetuity
The present value of an immediate annuity for 4 years at 10% p.a. compounded annually is ₹ 23,400. It’s accumulated value after 4 years would be ₹ ______
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 ______
An annuity in which each payment is made at the end of period is called ______
The intervening time between payment of two successive installments is called as ______
A 35-year old person takes a policy for ₹ 1,00,000 for a period of 20 years. The rate of premium is ₹ 76 and the average rate of bonus is ₹ 7 per thousand p.a. If he dies after paying 10 annual premiums, what amount will his nominee receive?
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`
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
