find the present value of 5,000 due in eight years if money is worth 12% compounded semi-annually compute also the compound interest
To find the present value of $5,000 due in eight years with a 12% interest rate compounded semi-annually, we can use the formula for the present value of a future amount:
Present Value = Future Value / (1 + (interest rate/frequency))^(years * frequency)
In this case, the interest rate is 12% (or 0.12), and it is compounded semi-annually, which means the frequency is 2. So let's plug in the values into the formula:
Present Value = $5,000 / (1 + (0.12/2))^(8 * 2)
First, let's simplify the fraction inside the parentheses:
Present Value = $5,000 / (1 + 0.06)^(16)
Next, we calculate the value inside the parentheses which is raised to the power of 16:
Present Value = $5,000 / (1.06)^(16)
Now, let's compute the value inside the parentheses raised to the power of 16:
Present Value = $5,000 / 1.222463
Finally, we divide $5,000 by 1.222463 to get the present value:
Present Value = $4,093.47
So, the present value of $5,000 due in eight years, with a 12% interest rate compounded semi-annually, is approximately $4,093.47.
To compute the compound interest, subtract the original principal amount (the present value) from the future value:
Compound Interest = Future Value - Present Value
= $5,000 - $4,093.47
= $906.53
Therefore, the compound interest for this investment is $906.53.