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Economics

Economics. Section 4 Dr.Hoda’s part Interest Sheet 5. Interest. 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.

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Economics

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  1. Economics Section 4Dr.Hoda’s part InterestSheet 5 Eng. RedaZein

  2. Interest • Interest ≡ Time value of money. • Interest is the fee charged by a lenderto a borrower for the use of borrowed money • It is usually expressed as an annual percentage of the principal. • Interest per year divided by principalamount, expressed as a percentage. also called interest rate.

  3. Interest types 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)

  4. Interest types 2- Discrete compounding interest: i: interest rate - Also if you have nominal interest rate use the law: Where:r: Nominal interest rate, m: # of interest periods per year N: # of years, m*N: Total number of interest periods

  5. Interesttypes 3- Continuous compounded interest: Where: r: Nominal annual interest rate N: # of years

  6. Interest types • 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.

  7. Let’s begin our sheet

  8. 1)An individual borrows $1000 at 12% compounded annually. If the loan is paid pack after 5 years, how much is repaid? (Ans.: S=$1762.34) 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)

  9. 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%)

  10. 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) ieff=22%)

  11. Any questions? 

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