Question

What is the nominal annual rate of interest compounded semi-annually at which $1598.00 will accumulate to $2425.39 in four years and six months? The nominal annual rate of interest is %. (Round the final answer to four decimal places as needed. Round all intermediate values to six decimal places as needed.)

Answer 1

To find the nominal annual rate of interest compounded semi-annually, we can use the formula for compound interest.

Step-by-step explanation:

To find the nominal annual rate of interest compounded semi-annually, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where A is the final amount, P is the principal amount, r is the nominal annual rate of interest, n is the number of times interest is compounded per year, and t is the number of years.

In this case, we have A = $2425.39, P = $1598.00, n = 2 (since interest is compounded semi-annually), and t = 4.5 years.

Plugging in the values, the equation becomes:

$2425.39 = $1598.00(1 + r/2)^(2*4.5)

Solving for r using algebra, we can isolate r and find the value which makes the equation true.