$3,700 is invested in an account with a 2.7% interest rate that is compounded quarterly. how much money is…

Explanation:

Step1: Recall the compound interest formula

The formula for compound interest is $A = P\left(1 + \frac{r}{n}\right)^{nt}$, where:

• $A$ is the amount of money accumulated after $n$ years, including interest.
• $P$ is the principal amount (the initial amount of money).
• $r$ is the annual interest rate (decimal).
• $n$ is the number of times that interest is compounded per year.
• $t$ is the time the money is invested for in years.

Step2: Identify the values given

• $P = 3700$ (the principal amount)
• $r = 2.7% = 0.027$ (convert percentage to decimal)
• $n = 4$ (compounded quarterly, so 4 times a year)
• $t = 1$ (one year)

Step3: Substitute the values into the formula

Substitute $P = 3700$, $r = 0.027$, $n = 4$, and $t = 1$ into the formula: [ A = 3700\left(1 + \frac{0.027}{4}\right)^{4\times1} ]

Step4: Calculate the value inside the parentheses first

Calculate $\frac{0.027}{4} = 0.00675$. Then $1 + 0.00675 = 1.00675$.

Step5: Calculate the exponent

Calculate $4\times1 = 4$. So we have $A = 3700\times(1.00675)^{4}$.

Step6: Calculate $(1.00675)^{4}$

First, calculate $1.00675^4$. Let's compute step by step:

• $1.00675^2 = 1.00675\times1.00675 \approx 1.0135455625$
• Then, $(1.0135455625)^2 \approx 1.027373$ (approximate value of $(1.00675)^4$)

Step7: Calculate the final amount $A$

Multiply the principal by the calculated value: $A = 3700\times1.027373 \approx 3700\times1.027373$. Calculate $3700\times1.027373$: $3700\times1.027373 = 3700 + 3700\times0.027373$ $3700\times0.027373 \approx 101.2801$ So $3700 + 101.2801 = 3801.2801$

Answer:

The amount of money in the account at the end of one year is approximately $$3801.28$.