Calculating Interest Rate. Find the interest rate implied by the following combinations of present and future values.

PresentValue Years Future Value
$400 11 $684
$183 4 $249
$300 7 $300

Since you do not state otherwise, I am assuming that your interest rate is compounded annually.
I will do the second of your questions.

Using Amount = Present Value(1+i)^n
we do not know i.

249=183(1+i)^4
1.3606557=(1+i)^4
take the fourth root
1.0800331=1+i
giving you i=0.0080031
so the annual rate is 8%

by observation the rate for you last question is clearly 0%

460 present 11 years 968 future value

To calculate the interest rate, you can use the formula:

Future Value = Present Value * (1 + Interest Rate)^Years

Let's go through each combination of present and future values to find the interest rate implied:

1) Present Value: $400, Years: 11, Future Value: $684
684 = 400 * (1 + Interest Rate)^11
Divide both sides by 400:
1.71 = (1 + Interest Rate)^11

To solve for the interest rate, take the 11th root of both sides:
(1 + Interest Rate) = 1.071
Subtract 1 from both sides:
Interest Rate = 0.071 or 7.1%

Therefore, the interest rate implied by the first combination is 7.1%.

2) Present Value: $183, Years: 4, Future Value: $249
249 = 183 * (1 + Interest Rate)^4
Divide both sides by 183:
1.36 = (1 + Interest Rate)^4

To solve for the interest rate, take the fourth root of both sides:
(1 + Interest Rate) = 1.08
Subtract 1 from both sides:
Interest Rate = 0.08 or 8%

Therefore, the interest rate implied by the second combination is 8%.

3) Present Value: $300, Years: 7, Future Value: $300
In this case, the future value remains the same as the present value, indicating that there is no growth or interest earned over the years.

Therefore, the interest rate implied by the third combination is 0%.

By following these steps, you can calculate the interest rate implied by different combinations of present and future values.

To calculate the interest rate for the first combination of values, we can use the formula:

Future Value = Present Value * (1 + i)^n,

where i is the interest rate and n is the number of years.

For the first combination, we have:

$684 = $400 * (1 + i)^11.

To solve for i, we can rearrange the equation:

(1 + i)^11 = 1.71 ($684 / $400).

Taking the 11th root of both sides, we get:

1 + i = 1.137058,

i = 0.137058.

So, the interest rate implied by the first combination of values is approximately 13.71%.

For the third combination, we have:

$300 = $300 * (1 + i)^7.

Simplifying the equation, we find:

1 + i = 1,

i = 0.

Therefore, the interest rate implied by the third combination of values is 0%.