Advertisements
Advertisements
Question
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
Solution
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
RELATED QUESTIONS
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 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 number of years for which an annuity of ₹500 is paid at the end of every year, if the accumulated amount works out to be ₹1,655 when interest is compounded annually at 10% p.a.
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]
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
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 :
Amount of money today which is equal to series of payments in future is called
______ is a series of constant cash flows over a limited period of time.
Fill in the blank :
The person who receives annuity is called __________.
Fill in the blank :
The payment of each single annuity is called __________.
Fill in the blank :
The intervening time between payment of two successive installments is called as ___________.
State whether the following is True or False :
Payment of every annuity is called an installment.
State whether the following is True or False :
The present value of an annuity is the sum of the present value of all installments.
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]
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
In ordinary annuity, payments or receipts occur at ______
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 ______
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
