English

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 - Mathematics and Statistics

Advertisements
Advertisements

Question

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 

Options

  • True

  • False

MCQ
True or False
Advertisements

Solution

True

shaalaa.com
Annuity
  Is there an error in this question or solution?
Chapter 2.2: Insurance and Annuity - Q.2

RELATED QUESTIONS

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]


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]


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]


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 :

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 ______. 


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 :

If payments of an annuity fall due at the beginning of every period, the series is called annuity __________.


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.


State whether the following is True or False :

Annuity contingent begins and ends on certain fixed dates.


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 :

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]


Multiple choice questions:

Rental payment for an apartment is an example of ______


Multiple choice questions:  

In annuity calculations, the interest is usually taken as ______


In ordinary annuity, payments or receipts occur at ______


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 ______


A company decides to set aside a certain sum at the end of each year to create a sinking fund, which should amount to ₹ 4 lakhs in 4 years at 10% p.a. Find the amount to be set aside each year?
[Given (1.1)4 = 1.4641]


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


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×