9. Looking forward - Future value 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 annuai, single year-end deposit. You are 30 years old now, so your money will grow for the next 35 years until you turn 65. You will open a savings account at the CitiBank 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 10.950 13.412 9% 15.190 15.937 12 20.140 15 Future Value of an Annuity Factor 3% 5% 6% 8% 11.460 12.578 13.180 14.487 14.190 15.917 16.370 18.977 18.600 21.578 23.270 27.152 26.870 33 066 36.780 45.762 36.460 47.726 54.850 73.105 47.570 66.438 79.060 113.282 60.450 90.318 111.430 172314 75.400 120.797 154.760 259.052 21.384 31.772 29.360 17.293 24.297 32.030 20 51.160 25 30 84.700 57.274 98.346 164.491 40.567 35 19.994 136 300 215.700 337.870 221.018 40 50.401 442 580 Complete the following 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 What will be the value of this money in 35 years? (Note: Round to two decimal places.) You began saving at age 30. If you had started five years earlier, so that your funds would grow for years, what would your nest egg be worth, assuming the same interest rate and annual savings amount? (Note: Round to two decimal places.) Suppose that a new bank in town offers 8% interest. How much would your yearly deposits be worth it you open a savings account there, assuming that your funds are invested for 35 years and all other factors remain the same? Complete the following table by entering relevant values. Then use either the table of future value factors, the future value formula, or your financia calculator 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 35 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 years? (Note: Round to two decimal places)
