Question

Total estimated cost of trip $45,500

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 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. (Note: Be sure to add the 5 additional years of inflation to the estimated future cost.) Write an explanation for your calculations so the reader is completely clear on how you derived your required monthly deposits.

Please show formula, do not excel use formatting

Answer 1

Total estimated cost of trip = 45,500 (today)

It is given inflation rate = 2.5% per annum.so estimated cost will increase 2.5% per year

Using future value = present value*(1+r)^n

r = inflation rate

n = number of periods

Cost of trip in 10 years(Future value)= 45500*(1+2.5%)^10

= 58,243.85

(NOTE: it is assumed that value for cost of trip given is for current period)

Future value of annuity = P*[(1+r)^n - 1 / r ]

p = monthly savings

r = rate of interest per period = 10% / 12 = 0.8333%

n = number of periods

58,243.85 = P*[(1+0.8333%)^120 - 1 / 0.8333% ]

Monthly savings(p) = $284.33

If trip is delayed for 5 years then future value =

45500*(1+2.5%)^15 = 65,897.57

Using future value of annuity formula

65,897.57 = P*[(1+0.8333%)^180 - 1 / 0.8333% ]

Monthly savings (P) = $159

(It is assumed that monthly deposits occur at the end of each month)

in case of any further explanation please comment.thankyou