Your sister just deposited $14,000 into an investment account. She believes that she will earn an annual return of 10.5 percent for the next 9 years. You believe that you will only be able to earn an annual return of 9.8 percent over the same period. How much more must you deposit today in order to have the same amount as your sister in 9 years

You must deposit $14,824.07

Explanation:

Giving the following information:

Sister:

Investment = $14,000

Interest rate = 10.5%

Number of years = 9

You:

Investment=?

Interest rate = 9.8%

Number of years = 9

First, we need to calculate the future value of your sister:

FV = PV * (1+i) ^n

FV = 14,000 * (1.105^9) = $34,386.55

Now, we can determine your deposit:

PV = FV / (1+i) ^n

PV = 34,386.55 / (1.098^9) = $14,824.07