Question

What is the future value of $2,000 after three years if the appropriate interest rate is 8% compounded semiannually?

Answer 1

Given: $2,000, 8% compounded semiannually, 3 years

To find the future value, we use the formula for compound interest:

`A=P(1+(i)/(n))^(nt)`

Where A is the total amount (in this case also the future value), P is the principal ($2,000), i is the interest rate (8% or 0.08), n is the number of compounding per year (2 because it is semi-annual) and t is the number of years (3).

Substituting the given, we get:

`\begin{gathered} A=2,000(1+(0.08)/(2))^(2(3)) \\ \\ A=2,000(1.04)^6 \\ \\ A=2,530.64 \end{gathered}`

So the future value of $2,000 after three years at 8% compounded semiannually is $2,530.64.