Question

A series of five payments in constant dollars, beginning with $6,000 at the end of the first year, are increasing at the rate of 5% per year. Assume that the average general inflation rate is 4%, and the market interest rate is 11%. What is the equivalent present worth of the series

Answer 1

Answer:

The equivalent present worth of the series is $27,714.

Explanation:

We have a series of five payments (n=5), paid at the end of the year, starting with $6,000 and increasing at a rate of 5% per year.

The inflation rate is 4% and the market interest rate is 11%.

The equivalent present worth of the series, where we take into account yearly increments and discount the value by inflation and interest rate, is:

$PV=\sum_{k=1}^5\frac{C_0(1+h)^{n-1}}{(1+i)^n(1+r)^n} \\\\PV=\frac{C_0}{(1+h)} \sum_{k=1}^5(\frac{(1+h)}{(1+i)(1+r)})^n$

Where:

h: increment in the payments (5%)

i: rate of inflation (4%)

r: market interest rate (11%)

Then,

$\frac{(1+h)}{(1+i)(1+r)}=\frac{1.05}{1.04*1.11}=\frac{1}{1.10} =0.91 \\\\\\PV=\frac{C_0}{(1+h)} \sum_{k=1}^5(\frac{(1+h)}{(1+i)(1+r)})^n\\\\PV=\frac{6,000}{1.05} \sum_{k=1}^50.91^n\\\\PV=5,714.3*(0.91+0.83+0.75+0.68+0.62)\\\\PV=5,714.3*3.8\\\\PV=21,714.3$