Question

week 3: introduction to compound interest
due sunday by 11:59pm points 10 submitting an external tool
suppose that $1200 is invested at $6\frac{1}{2}\\%$, compounded quarterly. how much is in the account at the end of 5 years?
round your answer to the nearest cent.
do not round until you calculate the final answer.
do not include the dollar sign.
sorry, thats incorrect. try again?
1652.27

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), \(n\) is the number of times interest is compounded per year, and \(t\) is the number of years.
Given \(P = 1200\), \(r=6.5\%=0.065\), \(n = 4\) (compounded quarterly), and \(t = 5\).

Step2: Substitute the values into the formula

$$
LATEXBLOCK0
$$

Step3: Calculate \((1.01625)^{20}\)

Using a calculator, \((1.01625)^{20}\approx1.382937\)

Step4: Calculate \(A\)

\(A=1200\times1.382937 = 1659.5244\)

Answer:

\(1659.52\)