Answer to Question #183823 in Financial Math for aqsa nabi

Question

FUTURE VALUE OF AN ANNUITY Your client is 40 years old; and she wants to begin saving for retirement, with the first payment to come one year from now. She can save $5,000 per year; and you advise her to invest it in the stock market, which you expect to provide an average return of 9% in the future.

a. If she follows your advice, how much money will she have at 65?

b. How much will she have at 70?

c. She expects to live for 20 years if she retires at 65 and for 15 years if she retires at 70. If her investments continue to earn the same rate, how much will she be able to withdraw at the end of each year after retirement at each retirement age?

Answer 1

(a)PV = Present Value 

I/Y = Interest rate for the period

n = Number of periods 

PMT = Each period cash flow

FV = Future Value 

Enter PV= 0

Enter PMT = -5000

Enter I/Y = 9% 

Enter N = 25 years (65-40)

Now Press CPT then FV = $423504.48 (rounded off)

Hence, She will have $423504.48 at 65.

(b)Enter PV= 0

Enter PMT = -5000

Enter I/Y = 9%

Enter N = 30 years 

Now Press CPT then FV = $681537.69 (rounded off)

Hence she will have $681537.69 at 70.

(c)

The money she will have at 65

$T = 65 - 40 = 25$

$FV=PMT\frac{(1+\frac{r}{n})^{t*n}−1}{\frac{r}{n}}$

$FV=5000\frac{(1+\frac{0.09}{1})^{25*1}−1}{\frac{0.09}{1}}$

$FV=423,504.5$

The money she will have at 70

$T = 70 - 40 = 30$

$FV=PMT\frac{(1+\frac{r}{n})^{t*n}−1}{\frac{r}{n}}$

$FV=5000\frac{(1+\frac{0.09}{1})^{30}−1}{\frac{0.09}{1}}$

$FV=681,537.7$

Payment when she retires at 65.

$PMT=\frac{PV\frac{r}{n}}{1−(1+\frac{r}{n})^{−t*n}}$

$PMT=\frac{423,504.5\frac{0.09}{1}}{1−(1+\frac{0.09}{1})^{−20*1}}=46,393.42$

Payment when she retires at 70

$PMT=\frac{PV\frac{r}{n}}{1−(1+\frac{r}{n})^{−t*n}}$

$PMT=\frac{681,537.7\frac{0.09}{1}}{1−(1+\frac{0.09}{1})^{−20*1}}=74,660.1$