Question

You plan to go to Asia to visit friends in three years. The trip is expected to cost a total of $10,000 at that time. Your parents have deposited $5,000 for you in a Certificate of Deposit paying 6% interest annually,maturing three years from now. Uncle Lee has agreed to pay for all remaining expenses. If you are going to put Uncle Lee's gift in an investment earning 10% over the next three years, how much must he deposit today, so you can visit your friends three years from today?
A. $3,039
B. $3,345
C. $5,801
D. $3,757

Answer 1

Answer:

A) $3,039

Explanation:

Total cost of trip= $10,000

Parent deposited $5,000 at 6% maturing 3 years.

Find the future value of parents deposit.

FV= PV×(1+i)^n

FV=future value

PV= present value= $5,000

I= interest rate=6%

n= no.of years = 3

FV= PV×(1+i)^n

= $5,000×(1+0.06)^3

=$5,000×(1.06)^3

= $5,000×1.191016

=$5,955.08

Balance=$10,000-$5,955.08

=$4,044.92

Uncle Lee agreed to pay for the remaining which is $4,044.92

Calculate uncle Lee's gift of 10% investment for 3 years

FV=PV×(1+i)^n

PV=FV/(1+i)^n

PV=$4,044.92/(1+0.10)^3

=$4,044.92/(1.10)^3

=$4,044.92/1.331

=$3,039.00826

Approximately $3,039