Question

Your sister just deposited $8,000 into an investment account. She believes that she will earn an annual return of 9.3 percent for the next 10 years. You believe that you will only be able to earn an annual return of 8.6 percent over the same period. How much more must you deposit today in order to have the same amount as your sister in 10 years?

Answer 1

$530.87

Explanation:

The computation of more amount is shown below:-

Before that we need to do the following calculations

As we know that

Future value = Present value × (1 + interest rate)^number of years

Future value of sister deposit is

= $8,000 × (1.093)^10

= $8,000 × 2.433

= $19,466.67

Future value of brother deposit is

= $8,000× (1.086)^10

= $8,000 × 2.2819

= $18,255.27

Now Difference in Future value is

= $19,466.67 - $18,255.27

= $1,211.40

So, Present value of the difference is

= Future value ÷ (1 + interest rate)^number of years

= $1,211.40 ÷ (1.086)^10

= $1,211.40 ÷ 2.2819

= $530.87