Assume the real rate of interest is 3.00% and the inflation rate is 2.00%. What is the value today of receiving $20,000.00 in seven years?

Answer 1

To find the present value (PV) of receiving $20,000 in seven years, we can use the formula for present value:

\[ PV = \frac{FV}{(1 + r)^n} \]

Where:

• \(PV\) = present value
• \(FV\) = future value ($20,000)
• \(r\) = real interest rate (3.00% or 0.03)
• \(n\) = number of years (7)

Now we can plug in the values:

\[ PV = \frac{20000}{(1 + 0.03)^7} \]

Calculating \( (1 + 0.03)^7 \):

\[ (1.03)^7 \approx 1.22504 \]

Then, we calculate the present value:

\[ PV = \frac{20000}{1.22504} \approx 16311.24 \]

Therefore, the value today of receiving $20,000 in seven years is approximately $16,311.24.

Answer 2

r is not 3%. That is the real rate =3% so how do you find r?

Answer 3

You are correct to point out that we need to find the nominal interest rate (r) when given the real interest rate and the inflation rate. We can use the Fisher equation to relate the nominal interest rate, real interest rate, and inflation rate:

\[ 1 + r = (1 + r_{real})(1 + i) \]

Where:

• \( r \) = nominal interest rate
• \( r_{real} \) = real interest rate (3% or 0.03)
• \( i \) = inflation rate (2% or 0.02)

Now we can calculate the nominal interest rate:

\[ 1 + r = (1 + 0.03)(1 + 0.02) \] \[ 1 + r = (1.03)(1.02) \] \[ 1 + r = 1.0606 \]

Thus, we find:

\[ r = 1.0606 - 1 = 0.0606 \text{ or } 6.06% \]

Now, we can use this nominal interest rate to find the present value of receiving $20,000 in seven years using the present value formula:

\[ PV = \frac{FV}{(1 + r)^n} \]

Substituting the values:

\[ PV = \frac{20000}{(1 + 0.0606)^7} \]

Calculating \( (1 + 0.0606)^7 \):

\[ (1.0606)^7 \approx 1.50363 \]

Then, calculate the present value:

\[ PV = \frac{20000}{1.50363} \approx 13,287.59 \]

Therefore, the value today of receiving $20,000 in seven years, considering a nominal interest rate of approximately 6.06%, is approximately $13,287.59.