Zahra deposits $\$ 620$ every year into an account earning an annual interest rate of $3.6 \%$ compounded annually. How much would she have in the account after $9$ years, 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. Zahra deposits

\$ 620

every year into an account earning an annual interest rate of

3.6 \%

compounded annually. How much would she have in the account after

9

years, 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 variables: Identify the variables from the problem to use in the formula. $\newline$ We have: $\newline$ $d = \$620$ (the amount invested at the end of each period) $\newline$ $i = 3.6\%$ or $0.036$ (the interest rate per period) $\newline$ $n = 9$ (the number of periods)
Convert interest rate: Convert the interest rate from a percentage to a decimal. $i = 3.6\% = \frac{3.6}{100} = 0.036$
Substitute values: Substitute the values into the formula to calculate the future value of the account. $\newline$ $A = d \times \left(\frac{(1 + i)^n - 1}{i}\right)$ $\newline$ $A = 620 \times \left(\frac{(1 + 0.036)^9 - 1}{0.036}\right)$
Calculate parentheses: Calculate the value inside the parentheses. $\newline$ $(1 + i)^n = (1 + 0.036)^9$
Calculate exponent: Calculate the exponent part of the formula. $\newline$ $(1 + 0.036)^9 \approx 1.036^9 \approx 1.368569$
Subtract one: Subtract $1$ from the result of Step $5$ . $\newline$ $1.368569 - 1 \approx 0.368569$
Divide by i: Divide the result of Step $6$ by $i$ . $\newline$ $0.368569 / 0.036 \approx 10.238583$
Multiply by $d$ : Multiply the result of Step $7$ by $d$ to find the future value $A$ . $A = 620 \times 10.238583 \approx 6347.9016$
Round result: Round the result to the nearest dollar. $\newline$ $A \approx \$(6348)$