Advertisements
Advertisements
प्रश्न
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]
उत्तर
Person buys the television for ₹20,000 in cash.
∴ First payment = ₹20,000
Remaining value of the television was paid in monthly instalments of ₹1,000.
∴ C= ₹1,000,
The duration of monthly installments is of 2 years.
∴ n = 24
Rate of interest is 12% p.a.
∴ r = `(12)/(12)` = 1% p.m.
∴ i = `"r"/(100) = (1)/(100)` = 0.01
The amount is paid at the end of every month.
∴ It is an immediate annuity.
Now, to find sum of all instalments we have to find present value.
∴ P = `"C"/"i"[1 - (1 + "i")^-"n"]`
∴ P = `(1,000)/(0.01)[1 - (1 + 0.01)^24]`
= 1,00,000 [1 – (1.01)–24]
= 1,00,000 (1 – 0.7875)
= 1,00,000 x 0.2125
∴ P = ₹21,250
∴ Cash price of the television = First Payment + Present Value
= 20,000 + 21,250
= ₹41,250
∴ Cash price of the television is ₹41,250.
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 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.
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 :
Rental payment for an apartment is an example of
Choose the correct alternative :
A retirement annuity is particularly attractive to someone who has
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 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.
Solve the following :
A shopkeeper insures his shop and godown valued at ₹5,00,000 and ₹10,00,000 respectively for 80 % of their values. If the rate of premium is 8 %, find the total annual premium.
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 ______
State whether the following statement is True or False:
Annuity contingent begins and ends on certain fixed dates
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 35-year old person takes a policy for ₹ 1,00,000 for a period of 20 years. The rate of premium is ₹ 76 and the average rate of bonus is ₹ 7 per thousand p.a. If he dies after paying 10 annual premiums, what amount will his nominee receive?
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. [Given (1.03)20 = 1.8061]
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`
