Dianelys deposits $\$ 6,100$ every year into an account earning an annual interest rate of $5 \%$ compounded annually. How much would she have in the account after $4$ 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. Dianelys deposits

\$ 6,100

every year into an account earning an annual interest rate of

5 \%

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

4

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: $\newline$ $d = \$6,100$ (the amount invested at the end of each period) $\newline$ $i = 5\%$ or $0.05$ (the interest rate per period) $\newline$ $n = 4$ (the number of periods)
Convert interest rate: Convert the percentage interest rate to a decimal. $i = 5\% = \frac{5}{100} = 0.05$
Plug values into formula: Plug the values into the compound interest formula to calculate the future value of the account. $\newline$ $A = d \times \left(\left(1 + i\right)^n - 1\right) / i$ $\newline$ $A = 6100 \times \left(\left(1 + 0.05\right)^4 - 1\right) / 0.05$
Calculate compound factor: Calculate the compound factor $(1 + i)^n$ . $(1 + i)^n = (1 + 0.05)^4$ $(1 + i)^n = 1.05^4$ $(1 + i)^n \approx 1.21550625$
Calculate numerator: Calculate the numerator of the formula: $((1 + i)^n - 1)$ .
$((1 + i)^n - 1) \approx 1.21550625 - 1$
$((1 + i)^n - 1) \approx 0.21550625$
Calculate future value: Calculate the future value of the account using the formula. $\newline$ $A \approx 6100 \times (0.21550625 / 0.05)$ $\newline$ $A \approx 6100 \times 4.310125$ $\newline$ $A \approx 26291.7625$
Round to nearest dollar: Round the future value to the nearest dollar. $\newline$ $A \approx \$26,292$