Section 4 Dr.Hoda’s part Interest Sheet 5 Eng. Reda Zein

  Interest ≡ Time value of money.  Interest is the fee charged by a lender to a borrower for the use of borrowed money  It is usually expressed as an annual percentage of the principal.  Interest per year divided by principal amount, expressed as a percentage. also called interest rate. Interest

 1- Simple interest: S=P(1+n*i) Where: P: Principal, the starting amount of money S: Future value, sum, resultant, final money, n: number of years (or period ) i: interest rate (it may be annual, every 6 months,every 3 months, monthly) ( note : that (S*n*i) is the increase on the original amount of money) Interest types

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  Notes: 1- Most of banks works by discrete interest type (As it has intermediate value). 2- Simple interest is favorable when you borrow money. 3- The continuous compounded is favorable in case of putting money in a bank. 4- In most of our problems we use discrete. 5- If he do not give you which type to use work with simple. Interest types

 Let’s begin our sheet

1)An individual borrows $1000 at 12% compounded annually. If the loan is paid pack after 5 years, how much is repaid? (Ans.: S=$ ) 2) Person A borrows $4,000 from person B and agrees to pay $1000 plus accrued interest at the end of the first year and $3,000 plus the accrued interest at the end of the fourth year. What are the amounts of the two payments if 8% annual interest applies? (Ans.: S1= $1080, S2=$3720)

3) Person A wishes to accumulate $1,000 in a saving account 4 years from now and the account pays interest at a rate of 9% compounded annually. How much must be deposited today? (Ans.: P=$708.43) 4) It is desired to have $9,000 available 12 years from now. If $5,000 is available for investment at the present time. What discrete annual rate of compound interest on the investment would be necessary to give the desired amount? (Ans.: i=5.02%)

5) What will be the total amount available 10 years from now if $2,000 is deposited at the present time with nominal interest at the rate of 6% compound semi-annually? (Ans.: S=$3612.2) 6) For the case of nominal annual interest rate of 20 %, determine: (a) The total amount to which one dollar of initial principle would accumulate after one year with continuous compounding. (b) The effective annual interest rate if compounding is continuous. (Ans.: (a)S=$1.22 (b) i eff =22%)

 Any questions?