Question

a. You plan to take a vacation in 10 months that will cost $8,167 How much do you have to invest today to just fund your vacation if your investments earn 4.7% APR (compounded monthly)?

b. You will have a property tax payment due in 10 months that will cost $8,292. How much do you have to invest today to have just enough to pay your property tax bill if your investments earn 4.9% APR (compounded monthly)?

Answer 1

Present Value:

Present value is current value of Future cash flows discounted at specified discount Rate.

PV = FV / (1+r)^n
Where r is Int rate per period
n - No. of periods

Part A:

Particulars	Amount
Future Value	$              8,167.00
Int Rate	0.3917%
Periods	10

Present Value = Future Value / ( 1 + r )^n
= $ 8167 / ( 1 + 0.0039 ) ^ 10
= $ 8167 / ( 1.0039 ) ^ 10
= $ 8167 / 1.0399
= $ 7853.91

Part B:

Particulars	Amount
Future Value	$              8,292.00
Int Rate	0.4083%
Periods	10

Present Value = Future Value / ( 1 + r )^n
= $ 8292 / ( 1 + 0.0041 ) ^ 10
= $ 8292 / ( 1.0041 ) ^ 10
= $ 8292 / 1.0416
= $ 7960.89