Savannah deposits $\$ 360$ every month into an account earning a monthly interest rate of $0.65 \%$ . How much would she have in the account after $8$ 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:

Full solution

Q. Savannah deposits

\$ 360

every month into an account earning a monthly interest rate of

0.65 \%

. How much would she have in the account after

8

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. $\newline$ We are given: $\newline$ $d$ (the amount invested at the end of each period) = $\$360$ $\newline$ $i$ (the interest rate per period) = $0.65\%$ or $0.0065$ in decimal form $\newline$ $n$ (the number of periods) = $8$ 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. $0.65\%$ as a decimal is $0.0065$ .
Substitute Values: Substitute the values into the formula. $\newline$ $A = 360 \times \left(\left(1 + 0.0065\right)^{8} - 1\right) / 0.0065$
Calculate $(1 + i)^n$ : Calculate the value inside the parentheses $(1 + i)^n$ . $(1 + 0.0065)^8 = 1.0065^8$
Calculate $(1 + i)^n$ : Calculate $(1 + i)^n$ using a calculator. $1.0065^8 \approx 1.0527$
Subtract $1$ : Subtract $1$ from the result of step $5$ . $\newline$ $1.0527 - 1 = 0.0527$
Divide by $i$ : Divide the result of step $6$ by $i$ . $\frac{0.0527}{0.0065} \approx 8.1077$
Multiply by $d$ : Multiply the result of step $7$ by $d$ . $360 \times 8.1077 \approx 2918.772$
Round to Nearest Dollar: Round the result to the nearest dollar. The future value of the account, rounded to the nearest dollar, is approximately $\$2919$ .