Question

Question 2
If the present value of $400 paid one year from now is $320, what is the one-year interest rate? (Note: this number is also known as the discount rate.)

*Make sure to input all percentage answers as numeric values without symbols, and use two decimal places of precision. For example, if the answer is 6%, then enter 0.06.

Answer 1

To find the one-year interest rate (or discount rate) given the present value (PV) of $400 paid one year from now, we can use the present value formula:

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

In this formula:
- \(PV\) is the present value,
- \(FV\) is the future value,
- \(r\) is the interest rate.

We know that:
- \(PV = 320\)
- \(FV = 400\)

Substituting the values into the formula gives us:

\[
320 = \frac{400}{(1 + r)}
\]

To solve for \(r\), first multiply both sides by \( (1 + r) \):

\[
320(1 + r) = 400
\]

Next, divide both sides by 320:

\[
1 + r = \frac{400}{320}
\]

Calculating the right side:

\[
1 + r = 1.25
\]

To find \(r\), subtract 1 from both sides:

\[
r = 1.25 - 1 = 0.25
\]

Converting this to a percentage gives:

\[
r = 0.25 = 25\%
\]

In the required format (numeric value without symbols), this is:

\[
0.25
\]

Thus, the one-year interest rate is \( \boxed{0.25} \).