Question

1. 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

Answer 1

$3,039

Step-by-step explanation:

Expected total cost=$10,000

Parents deposit=$5,000 maturing in three years

Find Value of parents deposits in three years

FV=PV×(1+I)^n

Where

FV=future value

PV=present value=$5,000

I=interest rate=6%

n=number of years=3

FV=$5,000×(1+0.06)^3

=$5,000×(1.06)^3

=$5000×1.191016

=$5,955.08

Balance=$10,000-$5,955.08

=$4,044.92

Uncle Lee is willing to pay the balance if the money is deposited in an investment that yields 10% annually.

Find uncle Lee's present value (PV)

FV=PV×(1+i)^n

PV=FV/(1+I)^n

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

=$4,044.92/(1.1,0)^3

=$4,044.92/1.331

=$3,039.0082

Approximately $3,039

Answer 2

The options:

A) $3,757

B) $3,039

C) $5,801

D) $3,345

The CORRECT ANSWER IS B)

B) $3,039

Step-by-step explanation:

Given,

Parents deposit (d) = $5,000

Interest rate (I) = 6%

Number of years of maturity (n) = 3 years

First, let's determine what the The Value of parents deposit in 3 years time will be;

Using,

Value = d × ( 1 + I)^n

The Value of parents deposit in 3 years time will be

= $5,000 × (1 + 0.06)^3

= $5,000 × 1.191016

= $5,955.08

Next,

let's estimate for Money short of travel cost at T3;

Using

Money short of travel cost at T3 = Total expected cost of trip - The Value of parents deposit in 3 years time

Where,

Total expected cost of trip = $10,000

The Value of parents deposit in 3 years time = $5,955.08

Money short of travel cost at T3 = ?

Therefore,

T3 = $(10000 - 5955)

T3 = $4044.92

Hence,

Money to be deposied at T0 to make up this shortfall = ?

Let's recall,

Uncle Lee's gift in an investment earning (I) = 10%

Number of years = three (3) years

Money short of travel cost at T3 = $4044.92

We will use the formula,

Money short of travel cost at T3

___________________________

( 1 + I)^n

To find the Money to be deposied at T0 to make up this shortfall

$4044.92

= __________

(1 + 0.10)^3

$4044.92

= __________

1.331

= $3,039.00826 (approximately $3,039)

The CORRECT ANSWER IS B)