Question

Your sister just deposited $12,000 into an investment account. She believes that she will earn an annual return of 10.1 percent for the next 8 years. You believe that you will only be able to earn an annual return of 9.4 percent over the same period. How much more must you deposit today in order to have the same amount as your sister in 8 years

Answer 1

The amounted must be deposited today = $12628.19

Step-by-step explanation:

The amount deposited by sister (present value) = $12000

Annual rate of return earned (r) = 10.1 %

Time ( n ) = 8 years

`\text{Total increased amount of sister after 8 years or future value} = PV(1 + r)^n \\`

`12000(1 + 10.1 Per cent)^8 \\`

`= 25910.74 dollar`

Now, in order to earn the same amount after 8 years with the interest rate of 9.4 percent. Therefore, the amount which is deposited at present will be:

`Present \ value = (Future \ value)/((1 + r)^n) \\`

`Present \ value = (25910.74)/((1 + 9.4 percent )^(8)) \\`

`= 12628.19 Dollar`

Therefore, $12628.19, is the amount that must be deposited by me.