Kiran deposits $\$ 380$ every month into an account earning a monthly interest rate of $0.35 \%$ . How much would he have in the account after $7$ 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. Kiran deposits

\$ 380

every month into an account earning a monthly interest rate of

0.35 \%

. How much would he have in the account after

7

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 variables: Identify the variables from the problem. $\newline$ We have: $\newline$ $d = \$380$ (the amount invested at the end of each period) $\newline$ $i = 0.35\%$ per month (the interest rate per period) $\newline$ $n = 7 \text{ years} \times 12 \text{ months/year} = 84 \text{ months}$ (the number of periods) $\newline$ $A = ?$ (the future value of the account we want to find)
Convert interest rate: Convert the interest rate from a percentage to a decimal. $i = 0.35\% = \frac{0.35}{100} = 0.0035$
Calculate future value: Use the formula to calculate the future value of the account. $A = d \times \left(\frac{(1 + i)^{n} - 1}{i}\right)$
Plug in values: Plug in the values and calculate the future value. $\newline$ $A = 380 \times \left(\left(1 + 0.0035\right)^{84} - 1\right) / 0.0035$
Calculate exponentiation: Calculate the value inside the parentheses and the exponent. $\newline$ $(1 + 0.0035)^{84} = 1.0035^{84}$
Continue calculation: Calculate the exponentiation. $1.0035^{84} \approx 1.3485$ (rounded to four decimal places for simplicity)
Calculate numerator: Continue with the calculation of $A$ . $A = 380 \times \left(\frac{1.3485 - 1}{0.0035}\right)$
Calculate future value: Calculate the numerator of the fraction. $\newline$ $1.3485 - 1 = 0.3485$
Perform division: Calculate the future value $A$ . $A = 380 \times (0.3485 / 0.0035)$
Multiply deposit amount: Perform the division. $\newline$ $0.3485 / 0.0035 \approx 99.5714$
Calculate final amount: Multiply by the monthly deposit amount. $\newline$ $A = 380 \times 99.5714$
Round final amount: Calculate the final amount. $A \approx 37837.13$
Round final amount: Calculate the final amount. $\newline$ $A \approx 37837.13$ Round the final amount to the nearest dollar. $\newline$ $A \approx \$(37837)$