Example Problems and Questions for Annuities

**Example 7.1**

A person pays *₹* 64,000
per annum for 12 years at the rate of 10% per year. Find the annuity [(1.1)^{12}=3.3184]

*Solution :*

**Example 7.2**

What amount should be deposited
annually so that after 16 years a person receives *₹*1,67,160 if the interest rate is
15% [(1.15)^{16}=9.358]

*Solution :*

**Example 7.3**

The age of the daughter is 2
years. Her father wants to get *₹*20,00,000 when his ward becomes
22 years He opens an account with a bank at 10% rate of compound interest. What
amount should he deposit at the end of every month in this recurring account?
[(1.0083)^{240}=6.194].

*Solution :*

*₹*3,209 is to be deposited at the
end of every month.

**Example 7.4**

A person deposits *₹*4,000 in
the beginning of every year. If the rate of compound interest is 14% then ,find
the amount after 10 years . [(1.14)^{10}=3.707]

*Solution :*

**Example 7.5**

A person purchases a machine on
1st January 2009 and agrees to pay 10 installments each of *₹*12,000 at
the end of every year inclusive of compound rate of 15%. Find the present value
of the machine. [(1.15)^{10}=4.016].

*Solution :*

**Example 7.6**

A photographer purchases a camera
on installments. He has to pay 7 annual installments each of *₹*36,000
right from the date of purchase. If the rate of compound interest is 16% then
find the cost price (present value) of the camera. [(1.16)^{7}=2.2828]

*Solution :*

**Example 7.7**

A person has taken a loan of *₹*7,00,000
at 16% rate of interest from a finance company. If the repayment period is of
15 years then find the installment he has to pay at the beginning of each
month. [(1.0133)^{180}=9.772]

*Solution :*

**Example 7.8**

The chairman of a society wishes
to award a gold medal to a student getting highest marks in Business
Mathematics. If this medal costs *₹*9,000 every year and the rate of
compound interest is 15% what amount is to be deposited now.

*Solution :*

Here *a* = 9,000 and *i* = 0.15

Therefore the amount to be
deposited is *₹* 60,000.

**Example 7.9**

A limited company wants to create
a fund to help their employees in critical circumstances. The estimated
expenses per month is *₹*18,000.Find the amount to be
deposited by the company if the rate of compound interest is 15%.

*Solution :*

Here *a* = 18,000 ; *i* = 0.15 and
*k* = 12.

Therefore the amount to be
deposited is *₹*14,40,000.

**Example 7.10**

Find the half yearly rate of
interest, to get a perpetuity of *₹*675 for every half yearly from
the present value of *₹*30,000/

*Solution :*

Here *P*=30,000 ; *a* = 675 ; *k* = 2, *i* = ?

**Exercise 7.1**

1. Find
the amount of an ordinary annuity of *₹*3,200 per annum for 12 years at
the rate of interest of 10% per year. [(1.1)^{12} = 3.3184]

2. If the
payment of *₹*2,000 is made at the end of every quarter for 10 years at the rate of 8%
per year, then find the amount of annuity. [(1.02)^{40}=2.2080 ]

3. Find
the amount of an ordinary annuity of 12 monthly payments of *₹*1, 500
that earns interest at 12% per annum compounded monthly. [(1.01)^{12} =
1.1262 ]

4. A bank
pays 8% per annum interest compounded quarterly. Find the equal deposits to be
made at the end of each quarter for 10 years to have *₹*30,200 ?
[(1.02)40 =2.2080]

5. A
person deposits *₹*2,000 from his salary towards his
contributory pension scheme. The same amount is credited by his employer also.
If 8% rate of compound interest is paid, then find the maturity amount at end of
20 years of service. [(1.0067)^{240} = 3.3266 ]

6. Find
the present value of *₹*2,000 per annum for 14 years at
the rate of interest of 10% per annum. [ (1.1)^{–14}= 0.2632]

7. Find
the present value of an annuity of *₹*900 payable at the end of 6
months for 6 years. The money compounded at 8% per annum. [(1.04)^{–12}=0.6252
]

8. Find
the amount at the end of 12 years of an annuity of *₹*5,000 payable at the beginning of
each year, if the money is compounded at 10% per annum.

9. What is the present value of
an annuity due of *₹*1,500 for 16 years at 8% per
annum? [ (1.08)15 = 3.1696 ]

10. What is the amount of
perpetual annuity of *₹*50 at 5% compound interest per
year?

Tags : Financial Mathematics , 11th Business Mathematics and Statistics(EMS) : Chapter 7 : Financial Mathematics

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11th Business Mathematics and Statistics(EMS) : Chapter 7 : Financial Mathematics : Example Problems for Annuities | Financial Mathematics

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