You want to travel to Europe to visit relatives when you graduate from university three years from now.The trip is expected to cost a total of $10 000.Your parents have deposited $5000 for you in a CD paying 6% interest annually, maturing three years from now.Aunt Hilda has agreed to finance the balance.If you are going to put Aunt Hilda's gift in an investment earning 10% annually over the next three years, how much must she deposit now so you can visit your relatives in three years?

Question

Quizplus · Accepted Answer

To find out how much Aunt Hilda needs to deposit now to cover the balance of the trip cost in three years, we first calculate the future value of the $5000 CD. Using the formula for future value, FV = PV(1 + r)^n, where PV is the present value, r is the annual interest rate, and n is the number of years, we find that the future value of the CD is $5000(1 + 0.06)^3 = $5955.08. The total cost of the trip is $10,000, so the balance needed is $10,000 - $5955.08 = $4044.92. To find out how much Aunt Hilda needs to deposit now to reach this amount in three years with a 10% annual interest rate, we rearrange the future value formula to solve for PV: PV = FV / (1 + r)^n. Substituting the values, we get PV = $4044.92 / (1 + 0.10)^3 = $3039. This means Aunt Hilda needs to deposit $3039 now.

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