Mackenzie deposits $\$ 690$ every month into an account earning a monthly interest rate of $0.25 \%$ . How much would she have in the account after $13$ months, 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. Mackenzie deposits

\$ 690

every month into an account earning a monthly interest rate of

0.25 \%

. How much would she have in the account after

13

months, 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. $\newline$ $d$ (the amount invested at the end of each period) = $\$690$ $\newline$ $i$ (the interest rate per period) = $0.25\%$ or $0.0025$ in decimal form $\newline$ $n$ (the number of periods) = $13$ months $\newline$ We will use these values in the formula $A=d\left(\frac{(1+i)^{n}-1}{i}\right)$ to find $A$ , the future value of the account.
Convert Interest Rate: Convert the interest rate from a percentage to a decimal. $\newline$ $0.25\% = \frac{0.25}{100} = 0.0025$ $\newline$ This is the value of $i$ that we will use in the formula.
Substitute Values into Formula: Substitute the values into the formula. $\newline$ $A = 690 \times \left(\left(1 + 0.0025\right)^{13} - 1\right) / 0.0025$ $\newline$ Now we will calculate the value inside the parentheses first.
Calculate $(1 + i)^{n}$ : Calculate the value of $(1 + i)^{n}$ . $(1 + 0.0025)^{13} = 1.0025^{13}$ We will use a calculator to find this value.
Calculate $1.0025^{13}$ : Calculate the value of $1.0025^{13}$ . $\newline$ $1.0025^{13} \approx 1.033$ $\newline$ This is the value we will use in the next step of our calculation.
Calculate $((1 + i)^{n} - 1)$ : Calculate the value of $((1 + i)^{n} - 1)$ . $\newline$ $1.033 - 1 = 0.033$ $\newline$ This is the value we will use in the next step of our calculation.
Calculate $(((1 + i)^{n} - 1) / i)$ : Calculate the value of $(((1 + i)^{n} - 1) / i)$ . $\newline$ $0.033 / 0.0025 = 13.2$ $\newline$ This is the value we will use in the next step of our calculation.
Calculate Future Value of Account: Calculate the future value of the account, $A$ . $A = 690 \times 13.2$ Now we will multiply to find the future value of the account.
Calculate Final Value of A: Calculate the final value of A. $\newline$ $A = 690 \times 13.2 \approx 9108$ $\newline$ We round to the nearest dollar as instructed in the problem.