Chloe deposits $\$ 750$ every month into an account earning a monthly interest rate of $0.4 \%$ . How much would she have in the account after $3$ years, to the nearest dollar? Use the following formula to determine your answer. $\newline$ $A=d\left(\frac{(1+i)^{n}-1}{i}\right)$ $\newline$ $A=$ the future value of the account after $n$ periods $\newline$ $d=$ the amount invested at the end of each period $\newline$ $i=$ the interest rate per period $\newline$ $n=$ the number of periods $\newline$ Answer:

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Math Problems

Grade 7

Compound interest

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Q. Chloe deposits

\$ 750

every month into an account earning a monthly interest rate of

0.4 \%

. How much would she have in the account after

3

years, to the nearest dollar? Use the following formula to determine your answer.

\newline

A=d\left(\frac{(1+i)^{n}-1}{i}\right)

\newline

A=

the future value of the account after

n

periods

\newline

d=

the amount invested at the end of each period

\newline

i=

the interest rate per period

\newline

n=

the number of periods

\newline

Answer:

Identify Given Values: Identify the given values from the problem. $\newline$ We are given: $\newline$ Monthly deposit $d$ = $\$750$ $\newline$ Monthly interest rate $i$ = $0.4\%$ or $0.004$ (as a decimal) $\newline$ Number of periods $n$ = $3$ years $* 12$ months/year = $36$ months $\newline$ We will use these values in the formula provided to calculate the future value of the account.
Convert Interest Rate: Convert the monthly interest rate from a percentage to a decimal. $\newline$ To do this, divide the interest rate by $100$ . $\newline$ $i = \frac{0.4\%}{100} = 0.004$
Calculate Future Value: Calculate the future value ( $A$ ) using the formula. $\newline$ $A = d \times \left(\frac{(1 + i)^{n} - 1}{i}\right)$ $\newline$ Substitute the given values into the formula. $\newline$ $A = 750 \times \left(\frac{(1 + 0.004)^{36} - 1}{0.004}\right)$
Calculate Value Inside: Calculate the value inside the parentheses. $\newline$ Calculate $(1 + i)^n$ . $\newline$ $(1 + 0.004)^{36}$
Perform Exponentiation: Perform the exponentiation. $\newline$ $(1 + 0.004)^{36} \approx 1.004^{36} \approx 1.154243$
Continue Calculation: Continue with the formula calculation. $\newline$ $A = 750 \times ((1.154243 - 1) / 0.004)$
Subtract One: Subtract $1$ from the result of the exponentiation. $\newline$ $1.154243 - 1 = 0.154243$
Divide by Interest Rate: Divide the result by the interest rate. $0.154243 / 0.004 = 38.56075$
Multiply by Deposit: Multiply by the monthly deposit amount. $A = 750 \times 38.56075$
Calculate Final Value: Calculate the final future value. $\newline$ $A \approx 750 \times 38.56075 \approx 28920.5625$
Round Future Value: Round the future value to the nearest dollar. $\newline$ $A \approx \$28921$