Simple Interest Compound Interest Annuities, Depreciation and Amortization

SUBJECT: MATHEMATICS

CLASS: SS 3

TERM: FIRST TERM

WEEK 9                                  Date: ……………………

Arithmetic of Finance:

• Simple Interest
• Compound Interest
• Annuities, Depreciation and Amortization

Simple Interest:

Interest: This is the amount paid on money borrowed. It is calculated as a percentage of the amount borrowed, at a particular rate and at a fixed period of time.

Hence; I = PRT

     100

Where; I = Interest, P = Principal, R = Rate and T= Time (calculated annually)

Examples:

1. Find the simple interest on #6000 for 4 years at 9% per annum.

Solution

I = PRT

100

I = 6000 x 4 x 9

100

= #2160

2. Find the amount if simple interest is paid on #150000 at 12% per annum for 3 years.

Solution:

I = 150000 x 12 x 3

100

=  #54000

Amount(A) = P + I = 150000 + 54000

A   = 204000

Evaluation:

1. Abu saved #8000 with a cooperative society. If simple interest is paid at 4.5% per annum, find the amount which Abu has in the society at the of 4 years.
2. A woman has #80000 in the Term Savings account for 3 years. How much interest does she receive at the end of the 3 years if she makes no withdrawal for the whole period?

Compound Interest

If a sum of money is invested for n years at a particular rate per annum compound interest, the amount A, after n years is given by the formula:

A = P(1 + r/100)ⁿ

Example:

1. Calculate the compound interest on #80000 for 2 years at 8.5% per annum.

Solution:

P = 80000, n = 2 years, r = 8.5%

A = 80000(1 + 8.5/100)²

= 80000(1.085 x 1.085)

A = 94178

C.I = 94178 – 80000

= #14178

1. A woman borrowed #500000 from a lender and pays interest at 12% per annum. If she repaid #100000 at the end of each year, what amount does she owe at the end of 2 years?

Solution:

P = 500000, r = 12%

Years 1: I = 500000 x 12 x 1

100

I = 60000

A = 500000 + 60000 = #560000

Repaid 100000, Amount = 560000 – 100000 = #460000

Year 2 :    I = 460000 x 12 x 1

100

I = #55200

Amount remaining: 460000 + 55200 = #515200 – #100000

Total Amount = #415200

Evaluation:

1. The sum of $180 is saved in an account which gives 9.5% per annum compound interest. Find the amount after 2 years, to the nearest cent.
2. The sum of #100000 is invested at 6% per annum compound interest, the interest being added half yearly. Find the amount after 2 years.

Annuities, Depreciation and Amortization

Example

1. A refrigerator costs #55000. What is its cost at the end of 3 years if the annual rate of depreciation is 20%?

Solution:

1^st year:

Value of refrigerator         #55000

20% depreciation          –     11000

44000

2^nd year:

Value                       44000

20% depreciation                  8800

35200

                  3^rd year:

                  Value                                35200

               20% depreciation            7040

                                                               28160

The cost at the end of the 3^rd year is #28160.

1. Find the amount of an annuity of #10000 paid yearly for 3 years at 8% per annum.

Solution:

1^st year annuity: #10000

Amount after 2^nd year = 10000(1 + 0.08)² = 10000 x 1.08²

2^nd year annuity after 1 year: 10000x 1.08

Total : 10000 + 10000 x 1.08  + 10000 x 1.08²  = #32464

Amount of annuity: #32464

Evaluation:

1. A television set costing #25000 depreciates by 15% in the first year and by 25% in the second year. Find its value after 2 years.
2. How long will it take for prices to double if the rate of inflation is 25% per annum?

General Evaluation

1. Using logarithm tables, find the compound interest on #20000 for 4 years at 12% per annum.
2. Calculate the amount of an annuity of #20000 payable yearly for 5 years at 12% per annum.

Reading Assignment: NGM for SS 3 Chapter 5 page 35 – 42

Weekend Assignment

1. Calculate the amount if simple interest is paid yearly at 15% per annum for 4 years on a principal of #550000
2. Calculate the compound interest on #18000 for 10 years at 9.5% per annum.
3. Find the amount created by an annuity of #60000 payable yearly for 4 years at 4% interest.
4. A woman insures her life for #3million by paying a premium of #2000 at the beginning of each year for 20 years. After 20 years the insurance company ends the agreement and gives her a lump sum payment of #50000. Assume compound interest at 8% per annum.

• Calculate the actual value of the premiums paid.
• Find the profit made by the company.

Which piece of numerical information is not needed in this problem?