Jason deposits $\$ 830$ every month into an account earning an annual interest rate of $3.9 \%$ compounded monthly. How much would he have in the account after $9$ 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. Jason deposits

\$ 830

every month into an account earning an annual interest rate of

3.9 \%

compounded monthly. How much would he have in the account after

9

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 Values: Identify the given values from the problem. $\newline$ Jason deposits $\$830$ every month into an account, so $d = \$830$ . $\newline$ The annual interest rate is $3.9\%$ , so the monthly interest rate $i = \frac{3.9\%}{12 \text{ months}} = 0.325\%$ per month. $\newline$ The number of periods $n = 9$ months.
Convert Interest Rate: Convert the annual interest rate to a decimal to use in the formula. $\newline$ $i = \frac{3.9\%}{100} = 0.039$ (annual rate in decimal) $\newline$ $i = \frac{0.039}{12}$ (monthly rate in decimal) $\newline$ $i \approx 0.00325$
Plug into Formula: Plug the values into the compound interest formula to calculate the future value $A$ . $A = d \times \left(\left(1 + i\right)^{n} - 1\right) / i$ $A = 830 \times \left(\left(1 + 0.00325\right)^{9} - 1\right) / 0.00325$
Calculate Exponent: Calculate the value inside the parentheses and the exponent. $\newline$ $(1 + 0.00325)^{9} \approx 1.02947$
Subtract One: Continue the calculation by subtracting $1$ from the result of the exponentiation. $\newline$ $1.02947 - 1 \approx 0.02947$
Divide by Rate: Divide the result by the monthly interest rate $i$ . $\newline$ $0.02947 / 0.00325 \approx 9.06769$
Multiply by Deposit: Multiply the result by the monthly deposit amount $d$ to find the future value $A$ . $A = 830 \times 9.06769$ $A \approx 7526.2027$
Round to Nearest Dollar: Round the future value $A$ to the nearest dollar. $A \approx \$(7526)$