noah opened a savings account and deposited $1,000.00. the account earns 11% interest, compounded annually…

noah opened a savings account and deposited $1,000.00. the account earns 11% interest, compounded annually. 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.

noah opened a savings account and deposited $1,000.00. the account earns 11% interest, compounded annually. 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

$P = 1000$, $r=0.11$ (since $11%=0.11$), $n = 1$ (compounded annually), $t = 3$.

Step2: Substitute into the compound - interest formula

$A=P(1 +\frac{r}{n})^{nt}=1000(1+\frac{0.11}{1})^{1\times3}$.

Step3: Calculate the value inside the parentheses first

$1+\frac{0.11}{1}=1 + 0.11=1.11$.

Step4: Calculate the exponent

$(1.11)^{3}=1.11\times1.11\times1.11 = 1.367631$.

Step5: Multiply by the principal

$A = 1000\times1.367631=1367.631$.

Step6: Round to the nearest cent

$A\approx1367.63$.

Answer:

$1367.63$