a.FV of $300 paid each 6 months for 5 years at a nominal rate of 12% compounded semiannually. Round your answer to the nearest cent
To find the future value (FV) of $300 paid every 6 months for 5 years, compounded semiannually at a nominal rate of 12%, you can use the formula for compound interest.
The formula for the future value of an investment with compound interest is:
FV = P * (1 + r/n)^(n*t)
Where:
FV = Future Value
P = Principal (initial investment or payment)
r = Nominal interest rate (in decimal form)
n = Number of compounding periods per year
t = Number of years
In this case, the principal (P) is $300, the nominal interest rate (r) is 12% (or 0.12 in decimal form), the compounding periods per year (n) is 2 (semiannually), and the number of years (t) is 5.
Plugging these values into the formula, we get:
FV = $300 * (1 + 0.12/2)^(2*5)
Simplifying the equation, we have:
FV = $300 * (1 + 0.06)^10
Calculating inside the parentheses first:
FV = $300 * (1.06)^10
Using a calculator, we can find that (1.06)^10 is approximately 1.790847, so:
FV = $300 * 1.790847
Multiplying these values together, we find:
FV = $537.25 (rounded to the nearest cent)
Therefore, the future value of $300 paid each 6 months for 5 years at a nominal rate of 12%, compounded semiannually, is approximately $537.25.