1 Translating Today’s Benefits to the Future w Suppose you want to know how much money you would have in 5 years if you placed $5,000 in the bank today at an interest rate of 6% compounded annually. w future value of a one-time investment. The future value is the accumulated amount of your investment fund at the end of a specified period.

2 w This is an exercise that involves the use of compound interest. Compound interest - Situation where you earn interest on the original investment and any interest that has been generated by that investment previously. Earn interest on your interest First year: $5,000(1+.06) = $5,300 Second year: $5,300(1+.06) = $5,618 Third year:$5,618(1+.06) = $5, Fourth year:$5,955.08(1+.06) = $6, Fifth year: $6,312.38(1+.06) = $6,691.13

3 Effect of Compound Interest

4 w Formula: FV = PV(1 + r) n r = interest rate divided by the compounding factor –(yearly r / compounding factor) n = number of compounding periods –(yearly n * compounding factor) PV = Present Value of your investment Compounding Factors: Yearly = 1 Quarterly = 4 Monthly = 12 Daily = 365

5 Please note that I will always report r’s and n’s as yearly numbers You will need to determine the compounding factor All of your terms must agree as to time. If you are taking an action monthly (like investing every month), then r and n must automatically be converted to monthly compounding. If you are rounding in time value of money formulas, you need AT LEAST four (4) numbers after the zeros (0) r =.08/12 r= (not or or etc.)

6 Yearly compounding PV = 5000 r =.06 n = 5 FV = $5,000(1.06) 5 = $6, Monthly compounding PV = 5000 r = (.06/12) =.005 n = 5(12) = 60 FV = $5,000(1+.005) 60 = $6,744.25

7 w _____ frequency of compounding = ___ FV w _____ length of investment = ____ FV w _____ interest rate = _____ FV Implications…

8 How do the calculations change if the investment is repeated periodically? w Suppose you want to know how much money you would have in 24 years if you placed $500 in the bank each year for twenty-four years at an annual interest rate of 8%. w future value of a periodic investment or future value of an annuity (stream of payments over time) = FVA

9 The formula is... where PV = the Present Value of the payment in each period r = interest rate divided by the compounding factor n = number of compounding periods

10 Let’s try it… w $500/year, 8% interest, 24 years, yearly compounding PV = 500 r =.08 n = 24 = 500 ( ) w = $33,382.38

11 Let’s try it again… w $50/month, 8% interest, 5 years, monthly compounding PV = 50 r = (.08/12) = n = 5(12) = 60

12 = 50 ( ) w = $ w Try again with n=120 w FVA=$

13 More Practice w You have a really cool grandma who gave you $1,000 for your high school graduation. You invested it in a 5-year CD, earning 5% interest. How much will you have when you cash it out if it is compounded yearly? w How much will you have if it is compounded monthly? w How much will you have if it is compounded daily?

14 w Yearly Compounding w 1,000(1+.05) 5 w =$1, w Monthly Compounding w r = (.05/12) = w n = 5(12) = 60 w 1,000( ) 60 w =$1, w Daily Compounding w r = (.05/365) = w n = 5(365) = 1,825 w 1,000( ) 1825 w =$1,284.00

15 Some more practice... w You have decided to be proactive for the future, and will save $25 a month. At the end of 10 years, how much will you have saved, if you earn 8% interest annually? w Monthly Compounding w FVA = w PV = $25 a month w r = (.08/12) = w n = (10)(12) = 120 w FVA = $4,573.65

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17 Rule of 72 w A handy formula to calculate the number of years it takes to double principal using compound interest is the Rule of 72. You simply divide the interest rate the money will earn into the number 72. For example, if interest is compounded at a rate of 7 % per year, your principle will double every 10.3 years. If the rate is 6 %, it will take 12 years.The rule of 72 also works for determining how long it would take for the price of something to double given a rate of increase in the price. For example, if college tuition costs are rising 8 % per year, the cost of college education doubles in just over nine years.