Question

please answer all and show all work.

6. You have just started working and would like to start saving for your retirement. If you would like to accumulate 53 million dollars when you retire in 40 years, how much do you need to save each month in cual amounts of the interest rate is 6% to reach this goal? Assume you start saving one month from today. Use the table of cash flows given below for problems 7 and 8. Cash Flow $1,075 $1,235 $1,510 $1,965 7 Find the present value of the cash flows if the interest rate is 9%. B. Find the future value of the cash flows in year 4 if the interest rate is 9% 9. Suppose you save $100 per month. How long will it take you to accumulate $10.000 if the annual interest rate is 5%7 10. Suppose you plan to save $5,000 per year for the 40 years you are working. How much can you withdraw in equal amounts each year for the 30 years you are retired. Assume that the interest rate is 10% and that you begin saving in one year.

Answer 1

6. we need to calculate monthly savings. so, interest rate will be monthly and period will also be in months.

Future value	$3,000,000
Period (in Years)	40
Interest rate	6%
Present value	$0
Monthly saving	$1,506.41

Calculation

А — 3000000 Future value Period (in Years) Interest rate Present value Monthly saving 0.06 =PMT(B4/12,B3*12,B5,-B2)

7 & 8. All the cash flows are assumed to be at the end of year.

Year	Cash flow	Present value	Future value
1	$1,075	$986.24	$1,392.16
2	$1,235	$1,039.47	$1,467.30
3	$1,510	$1,166.00	$1,645.90
4	$1,965	$1,392.06	$1,965.00
Total	$5,785.00	$4,583.77	$6,470.36

Calculation

For future value calculation, year 4 cash flow will not earn any interest because it is at the end of year 4.

Year WNA Cash flow 1075 1235 1510 1965 =SUM(B10:B13) Present value =B10/(1+9%) =B11/(1+9%)^2 =B12/(1+9%)^3 =B13/(1+9%)^4 =SUM(C10:C13) Future value =B10*(1+9%)^3 =B11*(1+9%)^2 =B12*(1+9%) -R13 14 Total =SUM(D10:D13)

9. No. of months and no. of years

Future value	$10,000
Monthly saving	$100
Interest rate	5%
Present value	$0
No. of months it wil take	129.63
No. of years it wil take	10.80

10000 0.05 Future value Monthly saving Interest rate Present value No. of months it wil take No. of years it wil take =NPER(B4/12,B3,B5,B2)-1 =B6/12

Formula is multiplied by -1 so that no. of months formula gives will be positive.

10. First we need to calculate future value of $5,000 yearly savings after 40 years. then we will use that future value to calculate yearly withdrawal for 30 years.

Period (in years)	40
Yearly saving	$5,000
Interest rate	10%
Present value	$0
Future value	$2,212,962.78
Period (in years)	30
Future value	$0
Interest rate	10%
Present value	$2,212,962.78
Yearly withdrawal	$234,749.43

Calculation

A 40 5000 Period (in years) Yearly saving Interest rate Present value Future value 0.1 =FV(B4,B2,-B3,B5) Period (in years) Future value Interest rate Present value Yearly withdrawal -B6 =PMT(B10,B8,-B11, B9)

In the future value calculation, PMT is negative so that formula gives the positive value. same in yearly withdrawal calculation.