You have decided that you want to be a millionaire when you retire in 44 years. If you can earn an annual return of 11.06 percent, how much do you have to invest today? What if you can earn an annual return of 5.53 percent?

Step-by-step explanation:

Let P represent the amount that you need to invest today. Thus, principal = $P

The return would be compounded annually. So

n = 1

The rate at which the principal would be compounded is 11.06%. So

r = 11.06/100 = 0.1106

The investment would be for 44 years. So

t = 44

The formula for compound interest is

A = P (1+r/n) ^nt

A = total amount in the account at the end of t years.

A = $1000000

Therefore

1000000 = P (1+0.1106/1) ^1*44

1000000 = P (1.1106) ^44

P = 1000000/101.05

P = $9896.1

2) if you can earn an annual return of 5.53 percent, then

r = 5.53/100 = 0.053

1000000 = P (1+0.53/1) ^1*44

1000000 = P (1.053) ^44

P = 1000000/9.7

P = $103093

1. Let amount deposited now be P.

So P * (1.1106^44) = 1,000,000, which means P=9896.06

2. Let amount deposited now be P.

So P * (1.0553^44) = 1,000,000, which means P=93639.42