$1000 accummualtes to $1500 in 5 years time and the rate of inflation is 3% p.a. What is the annual effective real rate of return?

The real rate of return is the annual percentage return realized on an investment, which is adjusted for changes in prices due to inflation.

Step 1: First, we need to calculate the nominal rate of return. This is the rate of return without adjusting for inflation. We can use the formula for the future value of a single sum:

FV = PV * (1 + r)^n

where: FV = future value of the investment ($1500) PV = present value of the investment ($1000) r = nominal rate of return n = number of periods (5 years)

We can rearrange this formula to solve for r:

r = [(FV / PV)^(1/n)] - 1

Substituting the given values:

r = [($1500 /$1000)^(1/5)] - 1 = 0.08447 or 8.447%

So, the nominal rate of return is 8.447% per year.

Step 2: Next, we need to calculate the real rate of return. This is the rate of return after adjusting for inflation. We can use the formula:

real rate = [(1 + nominal rate) / (1 + inflation rate)] - 1

Substituting the given values:

real rate = [(1 + 0.08447) / (1 + 0.03)] - 1 = 0.0529 or 5.29%

So, the annual effective real rate of return is 5.29%.