a principal of $5500 is invested in an account paying an annual rate of 6%. find the amount in the account…

a principal of $5500 is invested in an account paying an annual rate of 6%. find the amount in the account after 4 years if the account is compounded semiannually, quarterly, and monthly.\n(a) the amount in the account after 4 years if the account is compounded semiannually is $6967.24 (round to the nearest cent.)\n(b) the amount in the account after 4 years if the account is compounded quarterly is $ (round to the nearest cent.)

a principal of $5500 is invested in an account paying an annual rate of 6%. find the amount in the account after 4 years if the account is compounded semiannually, quarterly, and monthly.\n(a) the amount in the account after 4 years if the account is compounded semiannually is $6967.24 (round to the nearest cent.)\n(b) the amount in the account after 4 years if the account is compounded quarterly is $ (round to the nearest cent.)

Answer

Explanation:

Step1: Recall 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 $P = 5500$, $r=0.06$, and $t = 4$.

Step2: Determine $n$ for quarterly compounding

For quarterly compounding, $n = 4$.

Step3: Substitute values into the formula

$A=5500(1 +\frac{0.06}{4})^{4\times4}=5500(1 + 0.015)^{16}$.

Step4: Calculate the value inside the parentheses

$1+0.015=1.015$.

Step5: Calculate $(1.015)^{16}$

Using a calculator, $(1.015)^{16}\approx1.26898555$.

Step6: Calculate the final amount

$A = 5500\times1.26898555\approx6979.42$.

Answer:

$6979.42$