Kira has $\$ 500$ in an account that earns $15 \%$ interest compounded annually. $\newline$ To the nearest cent, how much interest will she earn in $3$ years? $\newline$ Use the formula $B=p(1+r)^{t}$ , where $B$ is the balance (final amount), $p$ is the principal (starting amount), $r$ is the interest rate expressed as a decimal, and $t$ is the time in years. $\newline$ $\$$ $\square$ $\newline$ Submit

Full solution

Q. Kira has

\$ 500

in an account that earns

15 \%

interest compounded annually.

\newline

To the nearest cent, how much interest will she earn in

3

years?

\newline

Use the formula

B=p(1+r)^{t}

, where

B

is the balance (final amount),

p

is the principal (starting amount),

r

is the interest rate expressed as a decimal, and

t

is the time in years.

\newline

\$

\square

\newline

Submit

Identify values for formula: First, let's identify the values we need to use in the formula $B=p(1+r)^t$ .
$p = \$500$ (the principal amount)
$r = 15\%$ or $0.15$ (the interest rate as a decimal)
$t = 3$ years (the time)
Plug values into formula: Now, plug the values into the formula to calculate the balance after $3$ years. $B = 500(1+0.15)^3$
Calculate value inside parentheses: Calculate the value inside the parentheses first. $1 + 0.15 = 1.15$
Raise to power of $3$ : Now raise $1.15$ to the power of $3$ . $\newline$ $1.15^3 = 1.520875$
Multiply principal by result: Multiply the principal amount by the result to find the balance. $\newline$ $B = 500 \times 1.520875$ $\newline$ $B = 760.4375$
Find interest earned: The balance after $3$ years is $\$760.4375$ , but we need to find the interest earned, not the total balance. $\newline$ Subtract the principal from the balance to find the interest. $\newline$ Interest = $B - p$ $\newline$ Interest = $760.4375 - 500$ $\newline$ Interest = $260.4375$
Round interest to nearest cent: Round the interest to the nearest cent. $\newline$ Interest = $\$260.44$