Compound growth of savings or investments 1

Interest: definition A. a sum paid or charged for the use of money or for borrowing money B.such a sum expressed as a percentage of money borrowed to be paid over a given period, usually one year. Source: dictionary.com 2

Two types of interest Simple interest: Fixed percentage of original amount invested or deposited. Compound interest: Fixed percentage of original amount plus accumulated interest. 3

Example: $1000 invested at 10% SimpleCompound Original Amount$1000 Year 1$1100 Year 2$1200$1210 Year 3$1300$1331 4

Simple v. compound Simple interest = linear growth Compound interest = exponential growth 5

Definitions: Balance: the current value of an account; equivalent to Y in exponential growth formula Principle: initial amount invested or deposited; equivalent to X in exponential growth formula 6

Basic formula for compound growth Balance=Principle(1+r) y Where: y = number of time periods of growth r= interest rate or rate of return (percentage expressed as decimal) 7

Solving for principle Balance/(1+r) y = Principle 8

Solving for y log (Balance/Principle)/log(1+r) = y 9

Solving for r ((Balance/principle)^(1/y))-1 = r 10

Compounding more than yearly Balance=Principle (1+r/n) yn 11

Compounding quarterly Balance=Principle (1+r/4) 4y 12

Compounding monthly Balance=Principle (1+r/12) 12y 13

5% APR, compounded quarterly, for 7 years Balance=Principle (1+.05/4) 28 14

5% APR, compounded monthly, for 7 years Balance=Principle (1+.05/12) 84 15

Annual percentage yield [APY] In formulas, r was annual percentage rate or APR When interest gets compounded more often than once per year, actual interest earned in a year is greater than APR 16

Example: $10,000 invested for 10 years at 8% APR Annually: $21, Quarterly: $22, Monthly: $22,

Computing APY 1.Compute the balance for two consecutive years at comparable point in time. 2.Calculate percentage change: (new balance-old balance)/old balance 18

Demonstration Chart to simulate growth in value of: $10,000 investment at 3% APR compounded monthly Open Excel file 19