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hboard | Rapidldentity $\newline$ IXL | Compound interest | $\newline$ Home $\newline$ ixl.com/math/grade $-8$ /compound-interest $\newline$ Liberty Hill Isd - Gal_ M Inbox ( $57$ )-jarosz.__ is: Core Ball! M $\quad$ S SHEIN Girls Letter G. $\newline$ $2065$ $-20$ Dark Royal. $\newline$ iberty Hill. $\newline$ My IXL $\newline$ Learning $\newline$ Assessment $\newline$ Analytics $\newline$ Eighth grade $>1.11$ Compound interest LSK $\newline$ Spencer deposited $\$ 10$ in an account earning $5 \%$ interest compounded annually. $\newline$ To the nearest cent, how much will he have 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. $\newline$ $\$$ $\newline$ Submit

Full solution

Q. hboard | Rapidldentity

\newline

IXL | Compound interest |

\newline

Home

\newline

ixl.com/math/grade

-8

/compound-interest

\newline

Liberty Hill Isd - Gal_ M Inbox (

57

)-jarosz.__ is: Core Ball! M

\quad

S SHEIN Girls Letter G.

\newline

2065

-20

Dark Royal.

\newline

iberty Hill.

\newline

My IXL

\newline

Learning

\newline

Assessment

\newline

Analytics

\newline

Eighth grade

>1.11

Compound interest LSK

\newline

Spencer deposited

\$ 10

in an account earning

5 \%

interest compounded annually.

\newline

To the nearest cent, how much will he have 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

\$

\newline

Submit

Identify Given Values: Identify the given values from the problem. $\newline$ Principal $p$ = $\$10$ $\newline$ Interest rate $r$ = $5\%$ or $0.05$ when expressed as a decimal $\newline$ Time $t$ = $3$ years $\newline$ We will use the compound interest formula $B = p(1 + r)^t$ to find the final balance $B$ .
Substitute Values: Substitute the given values into the compound interest formula. $\newline$ $B = 10(1 + 0.05)^3$ $\newline$ Now we need to calculate the value inside the parentheses first, which is $(1 + 0.05)$ .
Calculate Inside Parentheses: Calculate the value inside the parentheses. $\newline$ $1 + 0.05 = 1.05$ $\newline$ Now we have $B = 10(1.05)^3$ .
Calculate Exponent: Calculate the exponent part of the expression. $\newline$ $(1.05)^3 = 1.05 \times 1.05 \times 1.05$ $\newline$ We need to multiply $1.05$ by itself $3$ times.
Perform Multiplication: Perform the multiplication to find the value of $(1.05)^3$ . $1.05 \times 1.05 \times 1.05 = 1.157625$ Now we have $B = 10 \times 1.157625$ .
Multiply Principal: Multiply the principal by the result from Step $5$ to find the final balance. $\newline$ $B = 10 \times 1.157625$ $\newline$ $B = 11.57625$ $\newline$ To the nearest cent, we need to round the final balance.
Round Final Balance: Round the final balance to the nearest cent. $\newline$ $B \approx \$(11.58)$ $\newline$ Spencer will have approximately $\$(11.58)$ in his account after $3$ years.