tina is saving up money to buy a car. tina puts $10,000.00 into an account which earns 4% interest…

tina is saving up money to buy a car. tina puts $10,000.00 into an account which earns 4% interest, compounded monthly. how much will she have in the account after 3 years? 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.

tina is saving up money to buy a car. tina puts $10,000.00 into an account which earns 4% interest, compounded monthly. how much will she have in the account after 3 years? 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

$P = 10000$, $r=0.04$, $n = 12$, $t = 3$

Step2: Substitute values into formula

$A=10000\left(1+\frac{0.04}{12}\right)^{12\times3}$

Step3: Calculate the exponent part

$12\times3 = 36$, $\frac{0.04}{12}\approx0.00333$ $1+\frac{0.04}{12}=1 + 0.00333=1.00333$

Step4: Calculate the power part

$(1.00333)^{36}\approx1.12727$

Step5: Calculate the final amount

$A = 10000\times1.12727 = 11272.71$

Answer:

$11272.71$