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) = $5,955.08 Fourth year:$5,955.08(1+.06) = $6,312.38 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=0.006667 (not 0.0067 or 0.007 or etc.)

6. Yearly compounding PV = 5000 r =.06 n = 5 FV = $5,000(1.06) 5 = $6,691.13 Monthly compounding PV = 5000 r = (.06/12) =.005 n = 5(12) = 60 FV = $5,000(1+.005) 60 = $6,744.25

7. 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

8. 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

9. Let’s try it… w $500/year, 8% interest, 24 years, yearly compounding PV = 500 r =.08 n = 24 = 500 (66.7648) w = $33,382.38

10. Let’s try it again… w $50/month, 8% interest, 5 years, monthly compounding PV = 50 r = (.08/12) =.006667 n = 5(12) = 60

11. = 50 (73.4769) w = $3673.84 w Try again with n=120 w FVA=$9147.30

12. 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?

13. w Yearly Compounding w 1000(1+.05) 5 w =$1276.28 w Monthly Compounding w r = (.05/12) =.004167 w n = 5(12) = 60 w 1000(1+.004167) 60 w =$1283.36 w Daily Compounding w r = (.05/365) =.000136986 w n = 5(365) = 1825 w 1000(1+.000136986) 1825 w =$1284.00

14. 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) =.006667 w n = (10)(12) = 120 w FVA = $4573.65

16. Do I have the money now? Determining when to use Future Value vs. Present Value Calculation/Tables Yes No Is it a lump sum? Yes No Yes No Use FV of a single payment Use PV of a single payment Use FV of an annuity Use PV of an annuity Use FV calculation/table Use PV calculation/table

17. Future Value of $1 (single amount) Year5%6%7%8%9% 11.0501.0601.0701.0801.090 21.1031.1241.1451.1661.188 31.1581.1911.2251.2601.295 41.2161.2621.3111.3601.412 51.2761.3381.4031.4691.539 61.3401.4191.5011.5871.677 71.4071.5041.6061.7141.828 81.4771.5941.7181.8511.993 91.5511.6891.8381.9992.172 101.6291.7911.9672.1592.367 111.7101.8982.1052.3322.580 121.7962.0122.2522.5182.813 131.8862.1332.4102.7203.066 141.9802.2612.5792.9373.342 152.0792.3972.7593.1723.642 162.1832.5402.9523.4263.970 172.2922.6933.1593.7004.328 182.4072.8543.3803.9964.717 192.5273.0263.6174.3165.142 202.6533.2073.8704.6615.604

18. Year5%6%7%8%9% 11.000 22.0502.0602.0702.0802.090 33.1533.1843.2153.2463.278 44.3104.3754.4404.5064.573 55.5265.6375.7515.8675.985 66.8026.9757.1537.3367.523 78.1428.3948.6548.9239.200 89.5499.89710.26010.63711.028 911.02711.49111.97812.48813.021 1012.57813.18113.81614.48715.193 1114.20714.97215.78416.64517.560 1215.91716.87017.88818.97720.141 1317.71318.88220.14121.49522.953 1419.59921.01522.55024.21526.019 1521.57923.27625.12927.15229.361 1623.65725.67327.88830.32433.003 1725.84020.21330.84033.75036.974 1828.13230.90633.99937.45041.301 1930.53933.76047.37941.44646.018 2033.06636.78640.99545.76251.160 Future Value of a Series of Annual Deposits (annuity)

19. Year5%6%7%8%9% 10.9520.9430.9350.9260.917 20.9070.8900.8730.8570.842 30.8640.8400.8160.7940.772 40.8230.7920.7630.7350.708 50.7840.7470.7130.6810.650 60.7460.7050.6660.6300.596 70.7110.6650.6230.5830.547 80.6770.6270.5820.5400.502 90.6450.5920.5440.5000.460 100.6140.5580.5080.4630.422 110.5850.5270.4750.4290.388 120.5570.4970.4440.3970.356 130.5300.4690.4150.3680.326 140.5050.4420.3880.3400.299 150.4810.4170.3620.3150.275 160.4580.3940.3390.2920.252 170.4360.3710.3170.2700.231 180.4160.3500.2960.2500.212 190.3960.3310.2770.2320.194 200.3770.3120.2580.2150.178 Present Value of $1 (single amount)

20. Year5%6%7%8%9% 10.9520.9430.9350.9260.917 21.8591.8331.8081.7831.759 32.7232.6732.6242.5772.531 43.5463.4653.3873.3123.240 54.3294.2124.1003.9933.890 65.0764.9174.7674.6234.486 75.7865.5825.3895.2065.033 86.4636.2105.9715.7475.535 97.1086.8026.5156.2475.995 107.7227.3607.0246.7106.418 118.3067.8877.4997.1396.805 128.8638.3847.9437.5367.161 139.3948.8538.3587.9047.487 149.8999.2958.7458.2447.786 1510.3809.7129.1088.5598.061 1610.83810.1069.4478.8518.313 1711.27410.4779.7639.1228.544 1811.69010.82810.0599.3728.756 1912.08511.15810.3369.6048.950 2012.46211.47010.5949.8189.129 Present Value of a Series of Annual Deposits (annuity)