Arianna deposits $\$ 450$ every month into an account earning a monthly interest rate of $0.525 \%$ . How much would she have in the account after $24$ 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. Arianna deposits

\$ 450

every month into an account earning a monthly interest rate of

0.525 \%

. How much would she have in the account after

24

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. $\newline$ Arianna deposits $\$450$ every month, so $d = \$450$ . $\newline$ The monthly interest rate is $0.525\%$ , so $i = 0.525/100 = 0.00525$ . $\newline$ The number of periods is $24$ months, so $n = 24$ .
Convert Interest Rate: Convert the interest rate to a decimal. $\newline$ $i = 0.525\% = \frac{0.525}{100} = 0.00525$
Substitute Values: Substitute the values into the formula. $\newline$ $A = d \times \left(\frac{(1 + i)^{n} - 1}{i}\right)$ $\newline$ $A = 450 \times \left(\frac{(1 + 0.00525)^{24} - 1}{0.00525}\right)$
Calculate Future Value: Calculate the future value of the account after $24$ periods. $\newline$ $A = 450 * (((1 + 0.00525)^{24} - 1) / 0.00525)$ $\newline$ $A = 450 * (((1.00525)^{24} - 1) / 0.00525)$
Perform Exponentiation: Perform the exponentiation. $\newline$ $(1.00525)^{24} \approx 1.13269$
Continue Calculation: Continue the calculation. $\newline$ $A = 450 \times ((1.13269 - 1) / 0.00525)$ $\newline$ $A = 450 \times (0.13269 / 0.00525)$
Complete Division and Multiplication: Complete the division and multiplication. $\newline$ $A = 450 \times (25.274285714285715)$ $\newline$ $A \approx 11373.428571428572$
Round Final Answer: Round the final answer to the nearest dollar. $\newline$ $A \approx \$11373$