Advertisements
Advertisements
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]
उत्तर
Given, C = ₹ 24,000, Since amount is invested at the end of every 6 months for two years, it is an immediate annuity.
∴ n = 2 x 2 = 4 half years.
Rate of interest is 12% p.a
∴ r = `(12)/(2)` = 6% for six months
i = `"r"/(100) = (6)/(100)` = 0.06
Now, A = `"C"/"i"[(1 + "i")^"n" - 1]`
= `(24,000)/(0.06)[(1 + 0.06)^4 - 1]`
= `(24,000 xx 100)/(0.06 xx 100)[(1.06)^4 - 1`
= `(24,00,000)/6(1.2625 - 1)`
= 4,00,000 × 0.2625
∴ = 1,05,000
∴ Amount accumulated after 2 years is ₹ 1,05,000.
APPEARS IN
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 present value of an ordinary annuity of ₹63,000 p.a. for 4 years at 14% p.a. compounded annually. [Given (1.14)−4 = 0.5921]
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 rate of interest compounded annually if an annuity immediate at ₹20,000 per year amounts to ₹2,60,000 in 3 years.
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]
Choose the correct alternative :
A retirement annuity is particularly attractive to someone who has
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 :
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 :
Annuity certain begins on a fixed date and ends when an event happens.
Solve the following :
Find the amount a company should set aside at the end of every year if it wants to buy a machine expected to cost ₹1,00,000 at the end of 4 years and interest rate is 5% p. a. compounded annually. [(1.05)4 = 1.21550625]
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]
State whether the following statement is True or False:
An annuity where payments continue forever is called perpetuity
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 ______
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
