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Assume the real rate of interest is 2.00% and the inflation rate is 3.00%. What is the value today of receiving 13,546.00 in 15.00 years?

3 answers

To find the present value (PV) of receiving a future amount of money, we can use the formula for present value, which takes into account the interest rate and time period:

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

Where:

  • \( FV \) is the future value (the amount to be received in the future),
  • \( r \) is the real rate of interest,
  • \( n \) is the number of years until the amount is received.

In this case:

  • \( FV = 13,546.00 \),
  • \( r = 2.00% = 0.02 \),
  • \( n = 15.00 \) years.

Now, let's plug these values into the formula:

\[ PV = \frac{13,546.00}{(1 + 0.02)^{15}} \]

First, calculate \( (1 + 0.02)^{15} \):

\[ (1 + 0.02)^{15} = (1.02)^{15} \]

Calculating \( (1.02)^{15} \):

\[ (1.02)^{15} \approx 1.349353 \]

Now substitute this value back into the present value formula:

\[ PV \approx \frac{13,546.00}{1.349353} \]

Now calculate \( PV \):

\[ PV \approx 10,041.10 \]

Thus, the present value today of receiving \( 13,546.00 \) in \( 15.00 \) years is approximately \( 10,041.10 \).

What values do I enter for N, i/y, PV, PMT, and FV to solve on a finance calculator?

To use a financial calculator to determine the present value (PV) of receiving a future amount (FV), you would typically input the values as follows:

  • N (Number of periods): This is the total number of years until you receive the future amount. In your case, this would be 15.

  • I/Y (Interest rate per year): This is the real interest rate expressed as a percentage. In your case, it should be entered as 2.00.

  • PV (Present Value): Since you are solving for PV, you do not need to enter this value yet; however, when you are done calculating, this is the value you will obtain.

  • PMT (Payment): In this scenario, if there are no intermediate payments (like an annuity), you should enter 0.

  • FV (Future Value): This is the amount you will receive in the future. In your case, this would be 13,546.00.

After entering these values, the financial calculator should be set up as follows:

  • N = 15
  • I/Y = 2.00
  • PMT = 0
  • FV = 13,546.00

Then you would calculate for PV to find the present value of the future amount. After performing the calculation, the calculator should give you the present value, which we previously calculated to be approximately \( 10,041.10 \).