Question

On her 25th​ birthday, a young woman engineer decides to start saving toward building up a retirement fund that pays​ 6% interest compounded monthly​ (the market interest​ rate). She feels that​ $1,000,000 worth of purchasing power in​ today's dollars will be adequate to see her through her sunset years after her 65th birthday. Assume a general inflation rate of​ 4% per year.

​(a) If she plans to save by making 480 equal monthly​ deposits, what should be the amount of her monthly deposit in actual​ dollars? Assume the first deposit is made at the end of first month.

The amount of monthly deposit in actual dollars is

​$24112411.

​(Round to the nearest​ dollar.)

​(b) If she plans to save by making​ end-of-the-year deposits, increasing by​ $1,000 over each subsequent​ year, how much would her first deposit be in actual​ dollars?

The amount of the first deposit in actual dollars is

​$______????

​(Round to the nearest​ dollar.)

Answer 1

The amount required at the time of retirement

=1000000*(1+0.04)^40

= 4801020.628

Let first deposit annual deposit be A

increaing by 1000 every year Effective rate = (1+0.005)^12 -1 = 0.0616778

= 6.16778%

Now equation becomes

4801020628 = A *(F/A, 6.16778% , 40) + 1000 * (F/G, 6.16778%, 40)

4801020.628 = A * 161.442995 + 1000 *1968.990387

4801020.628 = A * 161.442995 + 1968990.387

A = (4801020.628 - 1968990.387) / 161.442995

A = 17541.98

= 17542 (round to nearest dollar)

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