Compound Interest Finance 321 Professor D’Arcy

Compound InterestFinance 321Professor D’Arcy Adam JohariLauren Dufour

Introduction to Compound Interest • Definition: interest that is calculated both on the principal as well as accumulated interest • Where is it used? • Loans, mortgages, annuities, etc… Why is it used? -It refers to the interest on interest principle.

Simple Interest • Definition: Interest calculated on solely the principal, and not off of past earned interest • Formula: I = Prt (where I = interest, P = principle, r = annual interest rate, t = time in years)

Compound Interest vs. Simple Interest

Compound Interest • Formula: FV = PV(1+r)n Explanation of Variables: FV = future value PV = present value r = annual interest rate n = number of compounding periods

Adjusting Interest Rates • Why do we have to adjust? • Interest rates are not always given to us as an annual percentage • They are sometimes stated as semi-annually, monthly, etc... How?

Adjusting Interest Rates • FV = PV (1 + r(n)/n)nt • r(n) = nominal interest rate • n = number of compounding periods in a year • t = time in years r(n)/n = is the effective interest rate for n periods

Adjusting Interest Rate Example • Find the future value of $500 invested for five years with a nominal interest rate of 8% compounded quarterly. FV = PV (1 + r (n) /n) nt FV = 500(1 + 0.08/4) 4*5 FV = $742.97

Timeline i = 6% n=0 n=1 n=2 PV FV

Timeline i = 6% n=0 n=1 n=2 $1000 $1123.6 FV = PV(1+i)n FV = 1000(1.06)2

Compound Interest Example 1 • Dyer needs $5000 five years from now to fund his Simpson collection. The current annual interest rate is 6%, and is expected to remain the same. How much would he have to invest today in order to reach his goal?

Solution to Example 1 • FV = $5000 • R = 6% • N = 5 • PV = ? FV = PV(1+r)n 5000 = PV(1.06)5 PV = $3736.29

Compound Interest Example 2 • Dyer invests $5000 today. The current nominal interest rate is 6%, which is compounded monthly. How much will he have 5 years from now?

Solution to Example 2 • PV = $5000 • R = 0.06/12 = 0.005 • N = 5*12 = 60 months • FV = ? FV = PV(1+r)n FV = 5000(1.005)60 FV = $6744.25

Continuous Compounding • Definition: Interest that is compounded on a continuous basis, rather than at fixed intervals • Formula: FV = PVect where e is approximately 2.718 where c is the continuously compounded interest rate *Note: c = ln(1+r), where r is the annual interest rate

Continuous Compounding Example • You have $400 and it grows at a continuous rate to $500 over 3 years. Find the continuously compounded interest rate.

Solution • FV = PVect • 500 = 400e c*3 • C = 7.44%

Question for the Class • Uncle Joe wants to purchase a Porsche at the end of the year 2008. Today is January 1, 2007. The Porsche is expected to cost $100000 on December 31, 2008. The current interest rate for 2007 is 7%, and the interest rate is expected to go up to 8% for the year 2008. On January 1, 2008, Aunt Edna promises to give Uncle Joe a $50000 New Years present. How much money would Uncle Joe need today in order to finance his dream car?

Thank You!

Compound Interest Finance 321 Professor D’Arcy