Question

Your dream vacation will cost $7,069. Using this amount answer the questions below.

1) Assuming that your estimated total cost will grow by 2.5% per year (due to inflation), demonstrate how you would compute the expected future cost of your dream vacation.

2) Suppose that you can invest money every month into a fee-free mutual fund and that this fund is expected to have a 10% nominal annual rate of return. Using your estimated future cost (including inflation) as future value, determine the amount of money you must save each month for the next 10 years (i.e., 120 months) to achieve your goal. Then, determine the monthly amount you must save if you delay your trip for an additional 5 years (that is, you will take the trip 15 years from today = 180 months) instead of 10 years from today.

Answer 1

Part (1):

Estimated cost on a future date is the Future Value ascertained adding compound interest at the rate specified, for the period involved. FV is calculated using the following formula:

FV= A*(1+r)^n

Where FV= Future value, A= Cost at the current level, r= Rate of inflation per period (say, year) and n= Period (number of years)

In the given case, A= $7,069. r= 2.5%.

Period is not specified.

In case the vacation takes place in 10 years (ie., n=10),

Estimated cost=$7,069*(1+2.5%)^10 = =$7,069*1.2800845 = $ 9,048.92

In case the vacation takes place in 15 years (ie., n=15),

Estimated cost=$7,069*(1+2.5%)^15 = =$7,069* 1.44829817 = $ 10,238.02

Part (2):

It is assumed that the nominal annual rate of return given is compounded monthly.

(a ): In case the vacation takes place in 10 years,

Estimated cost is $9,046.92 as given in pat (1).

Monthly savings required= $44.16 as follows:

(b ): In case the vacation takes place in 15 years,

Estimated cost is $10,238.02 as given in pat (1).

Monthly savings required= $24.70 as follows: