Find the future value of a $10,000 investment at 10 % annual interest compounded semiannually for 4 years.
(a) $ 14,000 (b) $ 12,000 (c) $ 24,774.55 (d) $ 14,774.55 (e) $ 24,477.55
Can someone please help me find the future value? I am stuck on this problem.
To find the future value of an investment, you can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A is the future value
P is the principal amount (initial investment)
r is the annual interest rate (as a decimal)
n is the number of times interest is compounded per year
t is the number of years
In this case, the principal amount (P) is $10,000, the annual interest rate (r) is 10% which is equivalent to 0.10 as a decimal, the number of times interest is compounded per year (n) is 2 (semiannually), and the number of years (t) is 4.
Using the formula, we can calculate the future value:
A = $10,000(1 + 0.10/2)^(2*4)
A = $10,000(1 + 0.05)^8
A = $10,000(1.05)^8
A ≈ $14,774.55
Therefore, the future value of a $10,000 investment at 10% annual interest compounded semiannually for 4 years is approximately $14,774.55.
So the correct answer is (d) $14,774.55.