Example Problems 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?