Question

John receives $400 in 1 year, $800 in two years, $1,200 in three

years and so on until the final payment of $4,000. Using an annual
effective interest rate of 6%, determine the present value of these

Answer 1

To determine the present value of the future cash flows, we can use the formula for the present value of an annuity. The formula is:

PV = C * (1 - (1 + r)^(-n)) / r

Where:
PV = Present Value
C = Cash flow received each year
r = Annual interest rate
n = Number of years

In this case, the cash flow received each year is increasing by $400, and the annual effective interest rate is 6%. Let's calculate the present value:

PV = $400 * (1 - (1 + 0.06)^(-1)) / 0.06 +
$800 * (1 - (1 + 0.06)^(-2)) / 0.06 +
$1200 * (1 - (1 + 0.06)^(-3)) / 0.06 +
$4000 * (1 - (1 + 0.06)^(-10)) / 0.06

Calculating this expression will give us the present value of the cash flows.