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Homework answers / question archive / Today you make an investment of $ 500 that pays 10% per year
Today you make an investment of $ 500 that pays 10% per year. If inflation is 2.5% per year, how much will you have in the account at the end of 20 years in current dollars and how much is the purchasing power based on year 0 (real dollars) of the money you have in the account at the end of 20 years.
Fill in the blanks:
Current dollars at the end of year 20 will be $ ____?____
The purchasing power of what is in the account at the end of year 20, based on year 0 (real dollars) is $ ___?____
1) Current dollars at end of 20 years = Present value(1+r)^n
r = rate of interest = 10%
n = no of years = 20
Present value = $ 500
Thus Current dollars at end of 20 years =500(1+10%)^20
=500(1+0.1)^20
=500(1.1)^20
=500 x 6.7275
= 3363.75 $
2) Now we need to find real interest rate
Real interest rate = (1+nominal interest rate)/(1+inflation rate) - 1
= (1+10%)/(1+2.5%) - 1
= 1.1/1.025 - 1
= 1.07317 - 1
= 0.07317
i.e 7.32%
Now The purchasing power of what is in the account at the end of year 20, based on year 0 (real dollars) = Present value(1+r)^n
r = rate of interest = 7.32%
n = no of years = 20
Present value = $ 500
Thus 500(1+7.32%)^20
= 500 x (1.0732)^20
= 500 x 4.1078
= 2053.92 $
