Question

You have decided that you want to be a millionaire when you retire in 45 years.

(a) If you can earn an annual return of 11.2 percent, how much do you have to invest today? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)
(b) What if you can earn an annual return of 5.6 percent? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Answer 1

for rate 11.2 percent ,principal = 8419.47

for rate 5.6 percent , principal = 86123.90

Step-by-step explanation:

given data

amount wish A = 1,000,000

time t = 45 year

rate r1 = 11.2 % = 0.112

rate r2 = 5.6 % = 0.056

to find out

how much do you have to invest today

solution

we know here amount formula that is

amount = Principal ×
`( 1+ r)^(t)` ..........................1

here r is rate and t is time so

for rate r1 principal amount is by equation 1 we get

amount = Principal ×
`( 1+ r)^(t)`

1,000,000 = Principal ×
`( 1+ 0.112)^(45)`

principal = 8419.47

and for rate r2 principal is from equation 1

amount = Principal ×
`( 1+ r)^(t)`

1,000,000 = Principal ×
`( 1+ 0.056)^(45)`

principal = 86123.90