Sam has $50$ $\$$ in an account that earns $5\%$ interest compounded annually. To the nearest cent, how much interest will he 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. Sam has

50

\$

in an account that earns

5\%

interest compounded annually. To the nearest cent, how much interest will he 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.

\$

____

Identify values for formula: Question_prompt: How much interest will Sam earn in $3$ years on $\$50$ with $5\%$ annual compound interest?
Plug values into formula: Step $1$ : Identify the values for the formula $B = p(1 + r)^t$ . Here, $p = \$50$ , $r = 5\%$ or $0.05$ as a decimal, and $t = 3$ years.
Calculate balance after $3$ years: Step $2$ : Plug the values into the formula to calculate the balance after $3$ years. $B = 50(1 + 0.05)^3$ .
Calculate $(1 + 0.05)^3$ : Step $3$ : Calculate $(1 + 0.05)^3$ . This is $1.05^3$ .
Find $1.05^3$ : Step $4$ : Use a calculator to find $1.05^3$ . The result is $1.157625$ .
Multiply principal by result: Step $5$ : Multiply the principal amount by the result from Step $4$ . $B = 50 \times 1.157625$ .
Find balance: Step $6$ : Perform the multiplication to find the balance. $B = \$$57$.$88125$.
Subtract original principal: Step $7$: To find the interest earned, subtract the original principal from the balance. $Interest = B - p$. $Interest = 57.88125 - 50$.
Calculate interest earned: Step $8$: Calculate the interest earned. Interest = $\$7.88125$.
Round interest to nearest cent: Step $9$: Round the interest to the nearest cent. The interest earned is $\$7.88$.