Tammy deposited $20$ $\$$ in an account earning $10\%$ interest compounded annually. To the nearest cent, how much interest will she earn in $3$ years? 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. $\$$ ____

Full solution

Q. Tammy deposited

20

\$

in an account earning

10\%

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

3

years? 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.

\$

____

Convert to Decimal: Tammy's principal $p$ is $\$20$ , the annual interest rate $r$ is $10\%$ , and the time $t$ is $3$ years. Convert the interest rate to decimal form by dividing by $100$ . $\newline$ $r = \frac{10\%}{100} = 0.10$
Compound Interest Calculation: Use the compound interest formula $B = p(1 + r)^t$ to calculate the balance after $3$ years. $\newline$ $B = 20(1 + 0.10)^3$
Calculate Inside Parentheses: Calculate the amount inside the parentheses first. $1 + 0.10 = 1.10$
Raise to Power: Now raise $1.10$ to the power of $3$ . $(1.10)^3 = 1.10 \times 1.10 \times 1.10$
Perform Multiplication: Perform the multiplication. $\newline$ $1.10 \times 1.10 \times 1.10 = 1.331$
Find Balance: Multiply the principal by the result to find the balance. $\newline$ $B = 20 \times 1.331$
Subtract Principal: Perform the multiplication to find the final balance. $\newline$ $B = 20 \times 1.331 = 26.62$
Calculate Interest Earned: To find the interest earned, subtract the original principal from the final balance. $\newline$ Interest earned = $B - p$ $\newline$ Interest earned = $26.62 - 20$
Calculate Interest Earned: To find the interest earned, subtract the original principal from the final balance. $\newline$ Interest earned = $B - p$ $\newline$ Interest earned = $26.62 - 20$ Perform the subtraction to find the interest earned. $\newline$ Interest earned = $26.62 - 20 = 6.62$