Question

Suppose a husband wants to take his wife on a trip three years from now to Europe to celebrate their 40th anniversary. He has just received a $25,000 inheritance from an uncle and intends to invest it for the trip. The husband estimates the trip will cost $30,500 and he believes he can earn 6% interest, compounded annually, on his investment.

Complete the following table to calculate the future value. Will he be able to pay for the trip with the accumulated investment amount?

Answer 1

To calculate the future value of the $25,000 investment with a 6% interest rate compounded annually over three years, we can use the compound interest formula:

FV = P(1 + r)^n

Where:

- (P) is the initial principal (the $25,000 inheritance)

- (r) is the annual interest rate (6% or 0.06 as a decimal)

- (n) is the number of years (3 in this case)

Let's calculate the future value:

FV = 25000(1 + 0.06)^3 approx 25000(1.191016) approx 29775.4

After three years, the investment will grow to approximately $29,775.4.

Now, let's compare this with the estimated cost of the trip, which is $30,500. Since the accumulated investment amount is less than the cost of the trip, the husband won't be able to fully cover the trip expenses with the accumulated investment amount. He would be short by approximately $724.6.

He might need to consider other sources of funds or adjust his plans for the trip.