Advertisements
Advertisements
प्रश्न
Find the rate of interest compounded annually if an annuity immediate at ₹20,000 per year amounts to ₹2,60,000 in 3 years.
Advertisements
उत्तर
Given, C = ₹20,000, A = ₹2,60,000, n = 3 years.
Now, A = `"C"/"i"[(1 + "I")^"n" - 1]`
∴ 2,60,000 = `(20,000)/"i"[(1 + "i")^3 - 1]`
∴ `(2,60,000)/(20,000) = (1)/"i" [1 + 3"i" + 3"i"^2 + "i"^3 - 1]`
∴ 13 = `(3"i" + 3"i"^2 + "i"^3)/"i"`
∴ 13 = 3 + 3i + i2
∴ i2 + 3i – 10 = 0
∴ i2 + 5i – 2i – 10 = 0
∴ i(i + 5) – 2(i + 5) = 0
∴ (i + 5)(i – 2) = 0
∴ i = – 5 or i = 2
But, i cannot be negative.
∴ i = 2
∴ `"r"/(100)` = 2
∴ r = 200% p.a.
∴ The rate of interest is 200% p.a.
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]
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]
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 plans to put ₹400 at the beginning of each year for 2 years in a deposit that gives interest at 2% p.a. compounded annually. Find the amount that will be accumulated at the end of 2 years.
Find the present value of an annuity due of ₹ 600 to be paid quarterly at 32% p.a. compounded quarterly. [Given (1.08)−4 = 0.7350]
Fill in the blank :
The person who receives annuity 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 :
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 least number of years for which an annuity of ₹3,000 per annum must run in order that its amount exceeds ₹60,000 at 10% compounded annually. [(1.1)11 = 2.8531, (1.1)12 = 3.1384]
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]
Solve the following :
Find the future value after 2 years if an amount of ₹12,000 is invested at the end of every half year at 12% p. a. compounded half yearly. [(1.06)4 = 1.2625]
Multiple choice questions:
Rental payment for an apartment is an example of ______
Multiple choice questions:
In an ordinary annuity, payments or receipts occur at ______
Multiple choice questions:
In annuity calculations, the interest is usually taken as ______
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
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
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 ______
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`
