Assume the real rate of interest is 4.00% and the inflation rate is 4.00%. What is the value today of receiving 12,330.00 in 13.00 years?

The value today of receiving 12,330.00 in 13.00 years = $ 4,425.97

Explanation:

Inflation is the increase in the price level. It erodes the value of money. rise in the price of money

Nominal interest is that quoted for investment or loan transactions. It has not been been adjusted for inflation.

Real interest rate is the amount of interest in terms of the the quantity of good and services that can be purchased. It is the nominal interest rate adjusted for inflation.

The relationship between inflation, real interest and nominal interest rate is given using the Fishers Effect;

N = ((1+R) * (1+F)) - 1

N - nominal rate, R-real rate, F - inflation

The Present Value (PV) of a future cash flow is the amount that needs to be invested today at a particular rate of return to equal the same cash flow in the future. Present value means the value in year 0 or now

PV = FV * (1+r) ^ (-n)

where FV - Future value, r - interest rate-, n - number of years

So all is set to answer the question:

first, we need to determine the nominal rate of interest using the real rate given:

N = ((1+R) * (1+F)) - 1

N = (1.04 * 1.04) - 1

= 8.2%

Finally, we work out the future value:

PV = FV * (1+r) ^ (-n)

FV - 12,330, r - 8.2%, n - 13

PV = 12,330 * (1.082) ^ (-13)

=$ 4,425.97

The value today of receiving 12,330.00 in 13.00 years = $ 4,425.97