Answer:
The equivalent present worth of the series is $27,211.16.
Explanation:
The first thing to do is to calculate the real interest using the following formula:
1 + i = (1 + r)(1 + inf) ..................... (1)
Where;
i = market interest rate = 11%, or 0.11
r = real interest rate = ?
inf = average general inflation rate = 4%, or 0.04
Substituting the values into equation (1) and solve for r, we have:
1 + 0.11 = (1 + r)(1 + 0.04)
1 + r = 1.11 / 1.04
1 + r = 1.06730769230769
r = 1.06730769230769 – 1
r = 0.06730769230769
The equivalent present worth of the series can now be calculated using the formula for calculating the present value (PV) of a growing annuity as follows:
PVga = (P / (r - g)) * (1 - ((1 + g) / (1 + r))^n) .................... (2)
Where;
PVga = present value of a growing annuity or equivalent present worth of the series = ?
P = constant dollar (or real-dollar) payments = $6,000
r = real interest rate = 0.06730769230769
g = growth rate of payments = 5%, or 0.05
n = number of years = 5
Substituting the values into equation (2), we have:
PVga = (6000 / (0.06730769230769 - 0.05)) * (1 - ((1 + 0.05) / (1 + 0.06730769230769))^5)
PVga = 346,666.666666712 * 0.078493722845371
PVga = $27,211.16
Therefore, the equivalent present worth of the series is $27,211.16.
