Use the compound interest formula Upper A equals Upper P left parenthesis 1 plus StartFraction r Over n EndFraction right parenthesis Superscript nt
to find the accumulated value of an investment of $ 15 comma 000 for 3 years at an interest rate of 4 % if the money is a. compounded semiannually; b. compounded quarterly; c. compounded monthly.
Question content area bottom
Part 1
a. What is the accumulated value if the money is compounded semiannually?
$
enter your response here (Round to the nearest cent as needed.)
The accumulated value of the investment compounded semiannually can be calculated using the formula A = P(1 + r/n)^(nt), where:
P = $15,000 (principal amount)
r = 4% (interest rate)
n = 2 (number of compounding periods per year, since semiannually means twice a year)
t = 3 (number of years)
Plugging in the values, we have:
A = 15000(1 + 0.04/2)^(2*3)
A = 15000(1 + 0.02)^(6)
A = 15000(1.02)^(6)
A ≈ $16,354.24
Therefore, the accumulated value if the money is compounded semiannually is approximately $16,354.24.