If $6,700 is invested at 4.6% interest compounded semi-annually, how much will the investment be worth in 15 years?

6700(1+.046/2)^(2*15) = 13253.90

$13,253.90

To calculate the future value of the investment, we will use the formula for compound interest:

\[A = P \left(1 + \frac{r}{n}\right)^{nt}\]

Where:
A = the future value of the investment
P = the principal amount (initial investment)
r = the annual interest rate in decimal form
n = the number of times interest is compounded per year
t = the number of years

Given:
P = $6,700
r = 4.6% or 0.046
n = 2 (semi-annually compounded)
t = 15

Let's substitute the values into the formula and calculate the future value:

\[A = 6700 \left(1 + \frac{0.046}{2}\right)^{(2)(15)}\]

\[A = 6700 \left(1 + 0.023\right)^{30}\]

\[A = 6700 \times (1.023)^{30}\]

Let's calculate (1.023)^30:

\[A = 6700 \times (1.8061)\]

\[A = 12,095.27\]

Therefore, the investment will be worth approximately $12,095.27 in 15 years.

To find the worth of the investment in 15 years, we can use the formula for compound interest:

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

where:
A = the future value of the investment
P = the principal amount invested ($6,700 in this case)
r = the annual interest rate (4.6% in this case, expressed as a decimal, 0.046)
n = the number of times interest is compounded per year (semi-annually, meaning twice a year)
t = the number of years the money is invested for (15 years in this case)

Now we can substitute the values into the formula and calculate the future value of the investment:

A = 6700(1 + 0.046/2)^(2*15)
A = 6700(1 + 0.023)^30

To simplify the calculation, we can add 1 to the interest rate per period:
1 + 0.023 = 1.023

A = 6700(1.023)^30

Using a calculator to evaluate (1.023)^30, we get approximately 1.7746.

A = 6700 * 1.7746
A = 11882.82

Therefore, the investment will be worth approximately $11,882.82 after 15 years.