Pedro deposits $\$ 880$ every month into an account earning a monthly interest rate of $0.675 \%$ . How much would he have in the account after $6$ 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. Pedro deposits

\$ 880

every month into an account earning a monthly interest rate of

0.675 \%

. How much would he have in the account after

6

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) = $\$880$ $\newline$ $i$ (the interest rate per period) = $0.675\%$ or $0.00675$ in decimal form $\newline$ $n$ (the number of periods) = $6$ 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 after $n$ periods.
Convert Interest Rate: Convert the interest rate from a percentage to a decimal. $0.675\%$ as a decimal is $0.675 / 100 = 0.00675$ .
Substitute Values: Substitute the values into the formula. $\newline$ $A = 880 \times \left(\left(1 + 0.00675\right)^{6} - 1\right) / 0.00675$
Calculate Inside Parentheses: Calculate the value inside the parentheses. $\newline$ Calculate $(1 + 0.00675)^{6}$ first. $\newline$ $(1 + 0.00675)^{6} \approx 1.040911$
Subtract Result: Subtract $1$ from the result obtained in Step $4$ . $\newline$ $1.040911 - 1 = 0.040911$
Divide by Interest Rate: Divide the result from Step $5$ by the interest rate. $\newline$ $0.040911 / 0.00675 \approx 6.059407$
Multiply by Amount: Multiply the result from Step $6$ by the amount invested per period. $\newline$ $880 \times 6.059407 \approx 5332.23816$
Round to Nearest Dollar: Round the result to the nearest dollar. $\newline$ The future value of the account after $6$ months, rounded to the nearest dollar, is approximately $\$5332$ .