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 $5,375.00 per year via an annual, 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:

Future Value of an Annuity Factor

Year	2%	3%	5%	6%	8%	9%	10%
10	10.950	11.460	12.578	13.180	14.487	15.190	15.937
12	13.412	14.190	15.917	16.870	18.977	20.140	21.384
15	17.293	18.600	21.578	23.270	27.152	29.360	31.772
20	24.297	26.870	33.066	36.780	45.762	51.160	57.274
25	32.030	36.460	47.726	54.860	73.105	84.700	98.346
30	40.567	47.570	66.438	79.060	113.282	136.300	164.491
35	49.994	60.460	90.318	111.430	172.314	215.700	271.018
40	60.401	75.400	120.797	154.760	259.052	337.870	442.580

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 if 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 financial 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.)

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.)