Martin has $\$ 3,582$ in an account that earns $5 \%$ interest compounded annually. $\newline$ To the nearest cent, how much will he have in $1$ year? $\newline$ 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. $\newline$ $\$$ $\square$

Full solution

Q. Martin has

\$ 3,582

in an account that earns

5 \%

interest compounded annually.

\newline

To the nearest cent, how much will he have in

1

year?

\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

Identify Given Values: Identify the given values from the problem. $\newline$ Principal $p$ = $\$3,582$ $\newline$ Interest rate $r$ = $5\%$ or $0.05$ when expressed as a decimal $\newline$ Time $t$ = $1$ year $\newline$ We will use the compound interest formula $B = p(1 + r)^t$ to find the balance after $1$ year.
Substitute Values: Substitute the given values into the compound interest formula. $\newline$ $B = (\$3,582)(1 + 0.05)^1$
Calculate Inside Parentheses: Calculate the value inside the parentheses. $\newline$ $1 + 0.05 = 1.05$
Raise to Power: Raise $1.05$ to the power of $1$ , which is simply $1.05$ since any number to the power of $1$ is the number itself. $\newline$ $1.05^1 = 1.05$
Multiply Principal: Multiply the principal by the result from Step $4$ to find the balance after $1$ year. $\newline$ $B = \$3,582 \times 1.05$
Perform Multiplication: Perform the multiplication to find the final balance. $\newline$ $B = \$3,761.10$