find the present value of the following future amount.
600,000 at 6% compunded semiannually for 25 years what is the present value
P = Po(1+r)^n
r = (6%/2)/100% = 0.03 = Semi-annual %
rate expressed as a decimal.
n = 2Comp,/yr. * 25yrs. = 50 Compounding periods.
Po(1.03)^50 = $600,000
Po*4.38391 = 600000
Po = $136,864.25 = Present value.
Plug the above values into the given Eq. and get $
To find the present value of a future amount, you can use the formula for the present value of a compound interest:
PV = (FV) / (1 + r/n)^(n*t)
Where:
PV = Present Value
FV = Future Value
r = Annual interest rate (as a decimal)
n = Number of compounding periods per year
t = Number of years
In this case, the future amount is $600,000, the interest rate is 6% (or 0.06 as a decimal), the compounding is semiannually (n = 2), and the time period is 25 years.
Plugging in these values into the formula, we can calculate the present value:
PV = (600,000) / (1 + 0.06/2)^(2*25)
Simplifying this equation, we have:
PV = (600,000) / (1.03)^(50)
Now we can calculate this using a calculator or a spreadsheet, raising 1.03 to the power of 50:
PV = (600,000) / 2.8531167
PV ≈ $210,246.98
Therefore, the present value of $600,000, with a 6% interest rate compounded semiannually for 25 years, is approximately $210,246.98.