christine opened a savings account and deposited $3,000.00. the account earns 8% interest, compounded…

christine opened a savings account and deposited $3,000.00. the account earns 8% interest, compounded monthly. if she wants to use the money to buy a new bicycle in 3 years, how much will she be able to spend on the bike? use the formula $a = p(1+\frac{r}{n})^{nt}$, where $a$ is the balance (final amount), $p$ is the principal (starting amount), $r$ is the interest rate expressed as a decimal, $n$ is the number of times per year that the interest is compounded, and $t$ is the time in years. round your answer to the nearest cent.

christine opened a savings account and deposited $3,000.00. the account earns 8% interest, compounded monthly. if she wants to use the money to buy a new bicycle in 3 years, how much will she be able to spend on the bike? use the formula $a = p(1+\frac{r}{n})^{nt}$, where $a$ is the balance (final amount), $p$ is the principal (starting amount), $r$ is the interest rate expressed as a decimal, $n$ is the number of times per year that the interest is compounded, and $t$ is the time in years. round your answer to the nearest cent.

Answer

Explanation:

Step1: Identify the values

$P = 3000$, $r=0.08$, $n = 12$, $t = 3$

Step2: Substitute into formula

$A=3000\left(1+\frac{0.08}{12}\right)^{12\times3}$ First, calculate $\frac{0.08}{12}\approx0.00667$. Then $1+\frac{0.08}{12}=1 + 0.00667=1.00667$. And $12\times3 = 36$. So $A = 3000\times(1.00667)^{36}$

Step3: Calculate the power

$(1.00667)^{36}\approx1.270237$

Step4: Calculate the final amount

$A=3000\times1.270237 = 3810.711$ Rounding to the nearest cent, $A\approx3810.71$

Answer:

$3810.71$