If the present value of $400 paid one year from now is $320, what is the one-year interest rate?
320(1+i)^1 = 400
1+i = 1.25
i = .25
State your conclusion.
To find the one-year interest rate, we can use the formula for present value:
Present Value = Future Value / (1 + Interest Rate)^Number of Periods
Given:
- Present Value = $320
- Future Value = $400
- Number of Periods = 1 year
We can rearrange the formula and solve for the interest rate:
$320 = $400 / (1 + Interest Rate)^1
Now, we need to isolate the interest rate. We can start by multiplying both sides of the equation by (1 + Interest Rate)^1:
(1 + Interest Rate)^1 * $320 = $400
Next, we can divide both sides of the equation by $320:
(1 + Interest Rate)^1 = $400 / $320
Simplifying:
(1 + Interest Rate) = 1.25
Now, subtract 1 from both sides of the equation to isolate the interest rate:
Interest Rate = 1.25 - 1
Interest Rate = 0.25
Therefore, the one-year interest rate is 0.25, or 25%.
To calculate the one-year interest rate, we need to use the formula for present value:
Present Value = Future Value / (1 + Interest Rate)^n
Where:
- Present Value is the value today ($320)
- Future Value is the value at a future time ($400)
- Interest Rate is the annual interest rate (unknown)
- n is the number of years (1)
To find the interest rate, we can rearrange the formula and solve for it:
Interest Rate = (Future Value / Present Value)^(1/n) - 1
Substituting the given values into the formula:
Interest Rate = ($400 / $320)^(1/1) - 1
Interest Rate = 1.25 - 1
Interest Rate = 0.25
Therefore, the one-year interest rate is 0.25, or 25%.