future amount needed $6,000 interest rate is 3% compounding period semiannually investment time 8 years what would the present value be
6000/(1+.03/2)^(2*8) = 4728.19
A loan of $6000at 8% is compounded semiannually for threethree years. Find the future value and compound interest. Use the $1.00 future value table or the future value and compound interest formulaBusiness Mathematics
To find the present value, we'll use the formula for compound interest:
Present Value = Future Value / (1 + r/n)^(nt)
Where:
Future Value = $6,000
Interest Rate = 3% = 0.03 (expressed as a decimal)
Compounding Period = Semiannually (twice per year)
Investment Time = 8 years
r = Interest Rate
n = Number of compounding periods per year
t = Investment time in years
First, let's determine the values of r, n, and t according to the given information.
r = 0.03 (interest rate of 3%)
n = 2 (semiannual compounding period)
t = 8 (investment time in years)
Now we can substitute these values into the formula:
Present Value = $6,000 / (1 + 0.03/2)^(2*8)
Let's calculate it step-by-step:
1. Inside the parentheses:
0.03/2 = 0.015
2. Calculate the exponent:
2 * 8 = 16
3. Raise the expression inside the parentheses to the power of 16:
(1 + 0.015)^16 = 1.015^16
4. Calculate the value inside the parentheses:
1.015^16 ≈ 1.2544
5. Divide the future value by the result from step 4:
$6,000 / 1.2544 ≈ $4,787.94
Therefore, the present value would be approximately $4,787.94.