Suppose $1 comma 500 is deposited in a bank account today (time 0), followed by $1 comma 500 deposits in years 2, 4, 6, and 8. At 9% annual interest, how much will the future equivalent be at the end of year 12?

$15,391.91

Explanation:

the first step is to find the present value of the cash flows. After the future value of the sum would be determined.

present value is the sum of discounted cash flows.

present value can be determined using a financial calculator

Cash flow in year 0 = $1500

Cash flow in year 1 = 0

Cash flow in year 2 = $1500

Cash flow in year 3 = 0

Cash flow in year 4 = $1500

Cash flow in year 5 = 0

Cash flow in year 6 = $1500

Cash flow in year 7 = 0

Cash flow in year 8 = $1500

I = 9%

PV = $5472.36

The formula for calculating future value:

FV = P (1 + r) n

FV = Future value  

P = Present value  

R = interest rate  

N = number of years  

$5472.36(1.09)^12 = $15,391.91

To find the PV using a financial calculator:

1. Input the cash flow values by pressing the CF button. After inputting the value, press enter and the arrow facing a downward direction.

2. after inputting all the cash flows, press the NPV button, input the value for I, press enter and the arrow facing a downward direction.  

3. Press compute  

the investment was $14,174.196

explanation:

a lump sum means that the father of the example made one deposit and leave it be.

we need to know the value of a capital that generated at 4.05% per year during 28 years the sum of $48,613.24

now clearing the formula to solve for capital we got:

and we reach the answer investment = $14,174.20