Adam deposits $\$ 200$ every month into an account earning a monthly interest rate of $0.675 \%$ . How much would he have in the account after $2$ 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. Adam deposits

\$ 200

every month into an account earning a monthly interest rate of

0.675 \%

. How much would he have in the account after

2

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 are given: $\newline$ $d = \$200$ (the amount invested at the end of each period) $\newline$ $i = 0.675\%$ per month (the interest rate per period) $\newline$ $n = 2$ years $* 12$ months/year $= 24$ periods (the number of periods) $\newline$ Now, convert the interest rate from a percentage to a decimal for the calculation. $\newline$ $i = 0.675\% = \frac{0.675}{100} = 0.00675$
Use formula: Use the formula to calculate the future value of the account. $\newline$ $A = d \times \left(\frac{(1 + i)^{n} - 1}{i}\right)$ $\newline$ Substitute the values into the formula. $\newline$ $A = 200 \times \left(\frac{(1 + 0.00675)^{24} - 1}{0.00675}\right)$
Calculate values: Calculate the value inside the parentheses and the exponent. $\newline$ Calculate $(1 + i)^{n}$ : $\newline$ $(1 + 0.00675)^{24} \approx 1.00675^{24}$ $\newline$ Use a calculator to find the value. $\newline$ $1.00675^{24} \approx 1.171603$
Continue calculation: Continue with the formula calculation. $\newline$ Now, subtract $1$ from the result obtained in the previous step. $\newline$ $1.171603 - 1 \approx 0.171603$
Complete formula: Complete the formula calculation. $\newline$ Divide the result by $i$ and multiply by $d$ . $\newline$ $A = 200 \times (0.171603 / 0.00675)$ $\newline$ Use a calculator to find the value. $\newline$ $A \approx 200 \times 25.422222$
Multiply amount: Multiply by the amount invested at the end of each period. $\newline$ $A \approx 200 \times 25.422222$ $\newline$ $A \approx 5084.4444$
Round final answer: Round the final answer to the nearest dollar. $\newline$ $A \approx \$5084$