Andy has $\$ 100$ in an account. The interest rate is $6 \%$ compounded annually. $\newline$ To the nearest cent, how much will he have in $2$ 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. $\newline$ $\$$ $\newline$ Submit $\newline$ Work it out $\newline$ Not feeling ready yet? These can help:

Full solution

Q. Andy has

\$ 100

in an account. The interest rate is

6 \%

compounded annually.

\newline

To the nearest cent, how much will he have in

2

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

\$

\newline

Submit

\newline

Work it out

\newline

Not feeling ready yet? These can help:

Identify Values: Identify the given values from the problem. $\newline$ Principal amount $p$ = $\$100$ $\newline$ Interest rate $r$ = $6\%$ or $0.06$ (as a decimal) $\newline$ Time $t$ = $2$ years $\newline$ We will use the compound interest formula $B = p(1 + r)^t$ to find the final balance.
Convert Interest Rate: Convert the interest rate from a percentage to a decimal. $\newline$ To convert a percentage to a decimal, divide by $100$ . $\newline$ $6\% = \frac{6}{100} = 0.06$
Substitute in Formula: Substitute the values into the compound interest formula. $\newline$ $B = p(1 + r)^t$ $\newline$ $B = 100(1 + 0.06)^2$
Calculate Inside Parentheses: Calculate the value inside the parentheses. $\newline$ $1 + 0.06 = 1.06$
Raise to Power: Raise $1.06$ to the power of $2$ . $(1.06)^2 = 1.06 \times 1.06 = 1.1236$
Multiply Principal Amount: Multiply the principal amount by the result from Step $5$ . $\newline$ $B = 100 \times 1.1236$ $\newline$ $B = 112.36$
Round Final Balance: Round the final balance to the nearest cent. The balance to the nearest cent is $\$112.36$ .