 A one time investment of $67,000 invested at 7% per year, compounded annually, will grow to $1 million in 40 years. Most graduates don’t have $67,000 available to invest. >Thus, others use regular investments and take advantage of compound interest. >A series of equal investments at regular time periods is called an ANNUITY

 EX. 1 $100 is deposited at the end of each month at 6% interest per year compounded monthly. MONTHSTARTING BALANCE INTEREST EARNED DEPOSITENDING BALANCE 1$0.00 $ $0.50$100.00$ $1.00$100.00$ $1.51$100.00$403.01

 Determine i, the interest rate per compounding period as a decimal, and n, the number of compounding periods for each annuity. TIME OF PAYMENTLENGTH OF ANNUITY INTEREST RATE PER YEAR FREQUENCY OF COMPOUNDING End of each year7 years3%Annually End of every 6 months (semi-annual) 12 years9%Semi-annually End of each quarter 8 years2.4% Quarterly End of each month5 years18% Monthly i = 0.03n = 1x7=7 n = 2x12=24 n = 4x8=32 n = 12x5=60

 How much money should you invest annually at 7% per year, compounded annually, to have $ by the time you retire? TVM Solver –

 Emily works part time and is saving for a car for college. She deposits $400 at the end of each month into an account that pays 3.6% interest per year, compounded monthly. How much will Emily have saved at the end of six months?

 Use Compound Interest Formula to calculate future value of each deposit.  1 st deposit: earns interest for 5 months.  2 nd deposit: earns interest for 4 months.  3 rd deposit: earns interest for 3 months. Etc… FV = PV(1 + i) n

FIRST DEPOSIT FV1 = $400(1.003) 5 =$ SECOND DEPOSIT FV2 = $400(1.003) 4 =$ THIRD DEPOSIT FV3 = $400(1.003) 3 =$ FOURTH DEPOSIT FV4 = $400(1.003) 2 =$ FIFTH DEPOSIT FV5 = $400(1.003) 1 =$ SIXTH DEPOSIT FV6 = $400(1.003) 0 =$400 Emily’s first deposit is made at the end of the 1 st month, so it earns interest for 5 months. Her second deposit earns interest for four months, and so on.

 Present Value for 1 st month of car: $227.20, but he will pay $  Present Value for 2 nd month of car: PV = FV(1 + i) -n =229.19( ) -2 = Thus the present value of the car for the 2 nd month is only $225.23, whereas he will pay $ The amount is getting less because there are less months to pay interest on every time.

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