$P(t) = 1,800(1.004)^t$ $\newline$ The function models $P$ , the amount of money, in dollars, in Yara's savings account $t$ years after she opened the account with an initial deposit of $\$1,800$ . How much money is in Yara's account $5$ years after her initial deposit if she makes no deposits or withdraws in that time? $\newline$ Choose $1$ answer: $\newline$ (A) $\$1,836.29$ $\newline$ (B) $\$1,873.31$ $\newline$ (C) $\$2,189.98$ $\newline$ (D) $\$9,036$

Full solution

P(t) = 1,800(1.004)^t

\newline

The function models

P

, the amount of money, in dollars, in Yara's savings account

t

years after she opened the account with an initial deposit of

\$1,800

. How much money is in Yara's account

5

years after her initial deposit if she makes no deposits or withdraws in that time?

\newline

Choose

1

answer:

\newline

(A)

\$1,836.29

\newline

(B)

\$1,873.31

\newline

(C)

\$2,189.98

\newline

(D)

\$9,036

Identify variables: Identify the variables in the function $P(t) = 1,800(1.004)^{t}$ . Here, $P(t)$ represents the amount of money in the account after $t$ years, and the initial amount is $\$1,800$ . The interest rate is compounded annually at a rate of $0.4\%$ (which is $1.004$ as a decimal).
Substitute value for $5$ years: Substitute the value of $t$ with $5$ years into the function to find out how much money Yara will have after $5$ years. $\newline$ $P(5) = 1,800(1.004)^{(5)}$
Calculate $(1.004)^5$ : Calculate the value of $(1.004)^5$ . $(1.004)^5 \approx 1.004^5 \approx 1.02020201$ (rounded to $8$ decimal places for accuracy)
Multiply initial amount: Multiply the initial amount by the calculated value from Step $3$ . $\newline$ $P(5) = 1,800 \times 1.02020201$ $\newline$ $P(5) \approx 1,800 \times 1.02020201 \approx 1,836.36362$
Round result to two decimal places: Round the result to two decimal places to represent money. $\newline$ P $5$ $\approx$ $\$1,836.36$