#4

Compounding Interest You know that paying yourself by depositing money in a savings account is a prudent start to your retirement plan. You determined that, based on your other obligations, you can save 5,000.00 per year via an annual, single year-end deposit. You are 40 years old now, so your money will grow for the next 25 years until you turn 55. You will open a savings account at the US Bank branch near your home. Its savings accounts are paying 6% interest The following table shows the future value factors for various periods and interest rates: Year 2% 10 10.950 13.412 9% 15.190 10% 15.937 12 20.140 21.384 15 17.293 Future Value of an Annuity Factor 3% 5% 6% 89 11.460 12.578 13.100 14.487 14.190 15.917 16.870 18.977 18.600 21.578 23.270 27.152 26,070 33.066 36.700 45.762 36.460 47.726 54.360 73.105 47.570 66,438 79.060 113.282 60.460 90.310 111.430 172314 75,400 120.797 154.760 259.052 20 25 24.297 32.030 40.567 29.360 51.160 34.700 136,300 215.700 337.670 31.772 57.274 98.346 164.491 271.018 30 35 49.994 40 60.401 442,500 Complete the following table by entering relevant values. Then use the table of future value factors to calculate the value of this nest egg $ Annual savings Years over which it will grow Interest rate Interest factor 6 What will be the value of this money in 25 years 7 (Note: Round to two decimal places) S $ Annual savings Years over which it will grow Interest rate Interest factor 96 What will be the value of this money in 25 years? (Note: Round to two decimal places. S You began savings at age 40. If you had started five years earlier, so that your funds would grow for be worth, assuming the same interest rate and annual savings amount? (Note: Round to two decimal places) years, what would your nest egg Suppose that a new bank in town offers 8% Interest. How much would your yearly deposits be worth if you open a savings account there, assuming that your funds are invested for 25 years and all other factors remain the same? Complete the following table by entering relevant values. Then use the table of future value factors to calculate the value of this nest egg. (Hint: Remember that the FVA factor is based on the new interest rate now.) $ Annual savings Years over which it will grow Interest rate Interest factor What will be the value of this money in 25 years? (Note: Round to two decimal places. S Again, if you had started your savings program five years earlier, what would your nest egg be worth, assuming that your funds were invested at this higher interest rate, the annual savings amount remains the same, and the funds are invested for years7 (Note: Round to two decimal places)