owen opened a savings account and deposited $100.00. the account earns 4% interest, compounded monthly. if…

owen opened a savings account and deposited $100.00. the account earns 4% interest, compounded monthly. if he wants to use the money to buy a new bicycle in 3 years, how much will he 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. $______

owen opened a savings account and deposited $100.00. the account earns 4% interest, compounded monthly. if he wants to use the money to buy a new bicycle in 3 years, how much will he 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

$P = 100$, $r=0.04$, $n = 12$, $t = 3$

Step2: Substitute values into formula

$A=100\left(1+\frac{0.04}{12}\right)^{12\times3}$ First, calculate the value inside the parentheses: $\frac{0.04}{12}\approx0.00333$, then $1+\frac{0.04}{12}=1 + 0.00333=1.00333$. Next, calculate the exponent: $12\times3 = 36$. So $A = 100\times(1.00333)^{36}$.

Step3: Calculate the final amount

$(1.00333)^{36}\approx1.12727$. Then $A=100\times1.12727 = 112.727$. Rounding to the nearest cent, $A\approx112.73$.

Answer:

$112.73$