###### Advertisements

###### Advertisements

**Solve the following :**

A man borrowed some money and paid back in 3 equal installments of ₹2,160 each. What amount did he borrow if the rate of interest was 20% per annum compounded annually? Also find the total interest charged. [(1.2)^{3} = 0.5787]

###### Advertisements

#### Solution

Given, C = ₹2,160, n = 3 years, r = 20% p.a.

∴ i = `"r"/(100) = (2)/(100)` = 0.2

Here, we have to find present value of annuity.

∴ P = `"C"/"i"[1 - (1 + "i")^-"n"]`

= `(2,160)/(0.2)[1 - (1 + 0.2)^-3]`

= 10,800[1 – (1.2)^{–3}]

= 10,800[1 – 0.5787]

= 10,800[0.4213]

∴ P = ₹4,550

The man has paid 3 equal instalments of ₹2,160 each.

∴ Total paid value of instalments

= 3 x 2,160

= ₹6,480

Interest = Total paid value of instalments – Present Value

= 6,480 – 4,550

= ₹1,930.

#### 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]

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 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]

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 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 :**

Amount of money today which is equal to series of payments in future is called

In an ordinary annuity, payments or receipts occur at ______.

**Choose the correct alternative :**

Rental payment for an apartment is an example of

**Fill in the blank :**

An annuity where payments continue forever is called __________.

**Fill in the blank :**

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

**State whether the following is True or False :**

Payment of every annuity is called an installment.

**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 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]

**Multiple choice questions:**

Rental payment for an apartment is an example of ______

**Multiple choice questions: **

In annuity calculations, the interest is usually taken as ______

**State whether the following statement is True or False:**

A sinking fund is a fund established by financial organization

**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

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 ______

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 ______

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]

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]

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`