By using the table in the handbook, the present value of $12,000 for six years compounded at 6 percent semiannually is: (Points : 2)
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To find the present value of $12,000 for six years compounded at 6 percent semiannually, you can use the formula for present value:
PV = FV / (1 + r/n)^(nt)
Where:
PV = Present Value
FV = Future Value
r = interest rate
n = number of compounding periods per year
t = number of years
In this case:
FV = $12,000
r = 6% = 0.06
n = 2 (compounded semiannually)
t = 6 years
Plugging in the values into the formula:
PV = 12000 / (1 + 0.06/2)^(2*6)
Simplifying the equation:
PV = 12000 / (1 + 0.03)^(12)
Now, we can use the table in the handbook to find the factor for (1 + 0.03)^(12):
From the table, the factor for (1 + 0.03)^(12) is 1.4297.
So, the present value of $12,000 for six years compounded at 6 percent semiannually is:
PV = 12000 / 1.4297
PV ≈ $8380.06
To find the present value of $12,000 for six years compounded at 6 percent semiannually, you can use the present value of an annuity formula or refer to a present value table.
Here's how you can calculate it using the present value of an annuity formula:
1. Convert the annual interest rate to the semiannual rate: 6 percent / 2 = 3 percent.
2. Determine the number of payment periods: 6 years * 2 (due to the compounding semiannually) = 12 semiannual periods.
3. Use the present value of an annuity formula:
Present Value = Payment Amount * (1 - (1 + Interest Rate)^(-Number of Periods)) / Interest Rate
In this case, the payment amount is $12,000 and the interest rate is 3 percent. Number of periods is 12.
Present Value = $12,000 * (1 - (1 + 0.03)^(-12)) / 0.03
4. Calculate the present value using a calculator or spreadsheet software.
Alternatively, you can use a present value table. The table will provide the present value factors for different interest rates and number of periods. Locate the 6% interest rate row and look for the factor corresponding to 12 periods, which represents the semiannual compounding. Multiply this factor by the payment amount of $12,000 to get the present value.
It's important to note that the specific value for the present value of $12,000 for six years compounded at 6 percent semiannually cannot be provided without the actual values from the present value table or the calculation.