Question

"Your sister just deposited $11,500 into an investment account. She believes that she will earn an annual return of 10 percent for the next 7 years. You believe that you will only be able to earn an annual return of 9.2 percent over the same period. How much more must you deposit today in order to have the same amount as your sister in 7 years?"

Answer 1

Answer:

I must deposit $12,103 today in order to have the same amount as your sister in 7 years.

Explanation:

Future value is the sum of principal amount and compounded interest amount invested on a specific rate for a specific period of time.

Use following formula to calculate the future value of invested amount

FV = PV x ( 1+ r )^n

Invested by my sister

FV = $11,500 x ( 1 + 10% )^7

Invested by me

FV = PV x ( 1 + 9.2% )^7

According to given condition

FV of my investment = FV of my sister's investment

PV x ( 1 + 9.2% )^7 = $11,500 x ( 1 + 10% )^7

PV x ( 1.092 )^7 = $11,500 x ( 1.10 )^7

PV x 1.85165 = $11,500 x 1.9487

PV x 1.85165 = $22410.05

PV = $22410.05 / 1.85165

PV  = $12,102.75 = $12,103