Question

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?

Answer 1

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

Answer 2

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 \( 10,041.10 \).

Answer 3

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 \( 10,041.10 \).