Present value equivalent for geometrically increasing series when the first year base of 4,000 increasing at 4% per year to year 15 at an interest rate 17% compounded continuously? urgent Help please
To find the present value equivalent for a geometrically increasing series, we need to use the formula for the present value of a growing annuity. The formula is:
PV = C * (1 - (1 + r)^(-n)) / (r - g)
Where:
PV = Present Value
C = Cash flow in the first year
r = Interest rate
n = Number of years
g = Growth rate
In this case, the cash flow in the first year is $4,000, the interest rate is 17% compounded continuously, and the growth rate is 4% per year. We need to find the present value equivalent for year 15.
First, we need to calculate the growth factor (GF) using the formula:
GF = (1 + g)^(n - 1)
GF = (1 + 0.04)^(15 - 1) = 2.543081
Next, we need to calculate the present value using the formula:
PV = C * (1 - (1 + r)^(-n)) / (r - g)
PV = $4,000 * (1 - (1 + 0.17)^(-15)) / (0.17 - 0.04)
PV = $4,000 * (1 - (1.17)^(-15)) / 0.13
PV = $4,000 * (1 - 0.124312) / 0.13
PV = $4,000 * 0.875688 / 0.13
PV = $4,000 * 6.736
PV = $26,944
Therefore, the present value equivalent for the geometrically increasing series from year 1 to year 15 is $26,944.