Answer:

Approximately 6.03%

Step-by-step explanation:

The formula for compound interest is as follows:

A=P(1+\frac{r}{n})^{nt}A=P(1+

n

r

)

nt

A = amount

P = principal

r = rate

n = times compounded per year

t = time in years

Adjust the formula and substitute the values in the given. Take note that the amount is the obtained interest plus the original principal.

A = 100,000 + 16,000 = 116,000

P = 100,000

r = ?

n = 2 (semi-annual)

t = 2.5 years

\begin{gathered}\frac{A}{P} = (1 + \frac{r}{n})^{nt}\\\sqrt[nt]{\frac{A}{P}} = 1 + \frac{r}{n}\\\sqrt[nt]{\frac{A}{P}} - 1 = \frac{r}{n}\\n(\sqrt[nt]{\frac{A}{P}} - 1) = r\\\\\\r = 2(\sqrt[2*2.5]{\frac{116,000}{100,000}} - 1)\\r = 2(\sqrt[5]{\frac{29}{25}} - 1)\\r \approx 2(1.03013 - 1)\\r \approx 2(0.03013)\\r\approx 0.06026\\r \approx6.03%\end{gathered}

Therefore, the nominal rate is approximately 6.03%.

Step-by-step explanation:

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Step-by-step explanation:

To solve this problem, you can use the formula for compound interest, which is:

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

where A is the amount after interest, P is the initial principal, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the time in years.

In this case, we know that:

A = P + interest = 100,000 + 16,000 = 116,000

P = 100,000

t = 2 1/2 years = 2.5 years

n = 2 (because the interest is compounded semiannually)

We can substitute these values into the formula and solve for r:

116,000 = 100,000(1 + r/2)^(2*2.5)

r = (116,000/100,000)^(1/(2*2.5)) - 1

r = 0.08 or 8% nominal rate

So, the nominal rate at which the amount was invested is 8% compounded semiannually.