Question

current learning objective: applying the compound - interest formula
question 6 practice similar questions
score: 0 of 1 point
find the final amount of money in an account if $5800 is deposited at 8% interest compounded semi - annually and the money is left for 7 years.
the final amount is $ enter your answer
(round answer to 2 decimal places)
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Explanation:

Step1: Identify the compound - interest formula

The compound - interest formula is \(A = P(1+\frac{r}{n})^{nt}\), where \(P\) is the principal amount, \(r\) is the annual interest rate (in decimal form), \(n\) is the number of times interest is compounded per year, and \(t\) is the number of years.
Given \(P=\$5800\), \(r = 8\%=0.08\), \(n = 2\) (semi - annually), and \(t = 7\) years.

Step2: Substitute the values into the formula

Substitute \(P = 5800\), \(r=0.08\), \(n = 2\), and \(t = 7\) into \(A = P(1+\frac{r}{n})^{nt}\).
First, calculate \(\frac{r}{n}=\frac{0.08}{2}=0.04\) and \(nt=2\times7 = 14\).
Then \(A=5800(1 + 0.04)^{14}\).

Step3: Calculate \((1 + 0.04)^{14}\)

Using a calculator, \((1+0.04)^{14}\approx1.731676\).

Step4: Calculate the value of \(A\)

\(A=5800\times1.731676\).
\(A = 5800\times1.731676=10043.7208\).

Answer:

\(10043.72\)