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

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

Step-by-step 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(C_0(1+h)^(n-1))/((1+i)^n(1+r)^n) \\\\PV=(C_0)/((1+h)) \sum_(k=1)^5(((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,

`((1+h))/((1+i)(1+r))=(1.05)/(1.04*1.11)=(1)/(1.10) =0.91 \\\\\\PV=(C_0)/((1+h)) \sum_(k=1)^5(((1+h))/((1+i)(1+r)))^n\\\\PV=(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`