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

Total= $14,572.964

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

We have to write a recursive formula that represents the number of books Ashley has at any time. At start Ashley has 100 books. If y is the number of books she has at any time, n is the number of books she wants to give away each week and x is the number of the weeks: y = 100 - n x . For example: n = 5. After 10 weeks: x = 10 and y = 100 - 5 * 10 = 100 - 50 = 50 books.  y = 100 - n x.