Question

You have decided to spend $5,100 on a vacation 3 years from now, $9,500 on a vacation 5 years from now, and $6,500 on a vacation 7 years from now. You want to deposit sufficient funds today to cover these future expenditures. How much do you need to deposit today if you can earn 7.6 percent on your savings

Answer 1

Total= $14,572.964

Step-by-step explanation:

Giving the following information:

Spendings:

Year 3= $5,100

Year 5= $9,500

Year 7= $6,500

Interest rate= 7.6 compunded annually.

We need to determine the initial investment to cover for 3 spendings.

We will calculate the present value of each payment, and sum them to determine the initial investment:

PV= FV/(1+i)^n

Year 3= 5,100/1.076^3= $4,093.864

Year 5= 9,500/1.076^5= $6,586.61

Year 7= 6,500/1.076^7= $3,892.49

Total= $14,572.964

TO prove it:

FV= PV*(1+i)^n

FV= (14,573*1.076^3) - 5,100= $13,054.56

FV= (13,054.56*1.076^2) - 9,500= $5,614.26

FV= (5,614.26*1.076^2) - 6,500= 0