Advertisements
Advertisements
प्रश्न
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.
Advertisements
उत्तर
Given, A = ₹41,000, C = ₹20,000, n = 2 years
We need to find r such that an ordinary annuity of ₹20,000 amounts to ₹41,000 in 2 years.
Since, A = `"C"/"i"[(1 + "i")^"n" - 1]`
41,000 = `"C"/"i"[(1 + "i")^2 - 1]`
41,000 = `(20,000)/"i"[(1 + "i")^2 - 1]`
`(41,000)/(20,000)= (1 + 2"i" + "i"^2 - 1)/"i"`
`(41)/(20) = ("i"^2 + 2"i")/"i"`
`(41)/(20)` = i + 2
`(41)/(20)` – 2 = i
`(41 - 40)/(20)` = i
∴ i = `(1)/(20)` = 0.05
But i = `"r"/(100)`
∴ 0.05 = `"r"/(100)`
∴ r = 5%
The rate of interest is 5%.
APPEARS IN
संबंधित प्रश्न
Find the accumulated (future) value of annuity of ₹ 800 for 3 years at interest rate 8% compounded annually. [Given (1.08)3 = 1.2597]
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]
Find the present value of an annuity immediate of ₹36,000 p.a. for 3 years at 9% p.a. compounded annually. [Given (1.09)−3 = 0.7722]
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]
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]
A person sets up a sinking fund in order to have ₹ 1,00,000 after 10 years. What amount should be deposited bi-annually in the account that pays him 5% p.a. compounded semi-annually? [Given (1.025)20 = 1.675]
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?
Choose the correct alternative :
Amount of money today which is equal to series of payments in future is called
Fill in the blank :
The person who receives annuity is called __________.
Fill in the blank :
The intervening time between payment of two successive installments is called as ___________.
Fill in the blank :
An annuity where payments continue forever is called __________.
Fill in the blank :
If payments of an annuity fall due at the end of every period, the series is called annuity __________.
State whether the following is True or False:
Annuity certain begins on a fixed date and ends when an event happens.
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 :
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]
Solve the following :
Find the present value of an annuity immediate of ₹20,000 per annum for 3 years at 10% p.a. compounded annually. [(1.1)–3 = 0.7513]
Solve the following :
A company decides to set aside a certain amount at the end of every year to create a sinking fund that should amount to ₹9,28,200 in 4 years at 10% p.a. Find the amount to be set aside every year. [(1.1)4 = 1.4641]
Solve the following :
After how many years would an annuity due of ₹3,000 p.a. accumulated ₹19,324.80 at 20% p. a. compounded yearly? [Given (1.2)4 = 2.0736]
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]
State whether the following statement is True or False:
The future value of an annuity is the accumulated values of all instalments
In ordinary annuity, payments or receipts occur at ______
If payments of an annuity fall due at the beginning of every period, the series is called annuity ______
The intervening time between payment of two successive installments is called as ______
