Simple and Compound Interest Interest is the income

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Simple and Compound Interest • Interest is the income earned by the lender from

Simple and Compound Interest • Interest is the income earned by the lender from the borrower is return of lending a specific amount of money(loan) for a specific period of time. • Interest rate is the cost of the borrowed money Interest rate = interest paid/ amount borrowed * 100 • This rate is always annual regardless of the length of the loan • Interest can be either simple or compounded.

1. Simple Interest • Interest is simple when it is not added at maturity

1. Simple Interest • Interest is simple when it is not added at maturity to the capital borrowed. Therefore, the borrower does not pay interest on interest. a. Simple interest for one year: Amount of interest = C *Interest rate I = C* it e. g: A person lends an amount of 1000, 000 to another person for 2 years at a rate of 8%. Find the amount of interest Interest for year 1 = 1000000*0. 08=80, 000 L. L Interest for year 2 = 1000000*0. 08= 80, 000 L. L Or I = 1000000*2*0. 08=160, 000 LL

1. Simple Interest b. Simple interest rate for months: I= (n * C*it)/12 n

1. Simple Interest b. Simple interest rate for months: I= (n * C*it)/12 n : number of months e. g: a bank lends an amount of 3000, 000 L. L over 6 months at simple rate of 7%. Interest = (6*3000000*0. 07)/12= 105, 000 LL c. Simple interest rate for days: A bank lends a person 9000000 for a period between 15 April and 1 July , i. e 77 days at a rate of 8%. Interest = 77* 9000000*0. 08/360= 154, 000 LL • Interest is annual regardless of the maturity of the loan.

2. Compound Interest • Interest rate is compound whenever the interest amount is added

2. Compound Interest • Interest rate is compound whenever the interest amount is added at the maturity to the original value of the loan. I. e the investor pays interest on the interest, since the interest amount is added to the capital borrowed and becomes part of it. a. Compound interest for one year : e. g: a bank lends a person 10, 000 for 2 years at a compound interest rate of 5%. find amount of interest. Interest = C [ (1+i)n – 1] Interest = 10000000[ (1+0. 05)^2 – 1] = 1025000 LL

2. Compound Interest b. Compound interest for months: Interest = C [ ( 1+i/12)n

2. Compound Interest b. Compound interest for months: Interest = C [ ( 1+i/12)n – 1] N= number of months e. g: a person borrowed a sum of 5000000 for 7 months at a compound rate of 12%. Interest amount = 5000000*[ (1+0. 12/12) 7 – 1] Interest = 360, 677 LL c. Compound interest for days: Interest = C [ ( 1+i/360)n – 1] N = number of days Ex: A loan of 7000, 000 for 50 days at 9%, will yield an interest of Interest = 7000000*[ (1+0. 09/360)50 – 1] = 8, 803, 809 LL

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