the principal represents an amount of money deposited in a savings account subject to compound interest at…

the principal represents an amount of money deposited in a savings account subject to compound interest at the given rate. a. find how much money there will be in the account after the given number of years. b. find the interest earned. principal: $3000 rate: 7% compounded: daily time: 4 years click the icon to view some finance formulas. formulas in the provided formulas, a is the balance in the account after t years, p is the principal investment, r is the annual interest rate in decimal form, n is the number of compounding periods per year, and y is the investments effective annual yield in decimal form. a = p(1 + r/n)^nt p = a/(1 + r/n)^nt a = pe^rt y=(1 + r/n)^n - 1 a. the amount of money in the account after 4 years is $ (round to the nearest hundredth as needed.)

the principal represents an amount of money deposited in a savings account subject to compound interest at the given rate. a. find how much money there will be in the account after the given number of years. b. find the interest earned. principal: $3000 rate: 7% compounded: daily time: 4 years click the icon to view some finance formulas. formulas in the provided formulas, a is the balance in the account after t years, p is the principal investment, r is the annual interest rate in decimal form, n is the number of compounding periods per year, and y is the investments effective annual yield in decimal form. a = p(1 + r/n)^nt p = a/(1 + r/n)^nt a = pe^rt y=(1 + r/n)^n - 1 a. the amount of money in the account after 4 years is $ (round to the nearest hundredth as needed.)

Answer

Explanation:

Step1: Identify the formula

Since the interest is compounded daily, we use the compound - interest formula $A = P(1+\frac{r}{n})^{nt}$, where $P=$3000$, $r = 0.07$ (7% in decimal form), $n = 365$ (number of compounding periods per year for daily compounding), and $t = 4$ years.

Step2: Substitute the values into the formula

$A=3000(1 +\frac{0.07}{365})^{365\times4}$. First, calculate the value inside the parentheses: $\frac{0.07}{365}\approx0.000191781$, then $1+\frac{0.07}{365}=1 + 0.000191781=1.000191781$. Next, calculate the exponent: $nt=365\times4 = 1460$. So, $A = 3000\times(1.000191781)^{1460}$. Using a calculator, $(1.000191781)^{1460}\approx1.323129$. Then $A=3000\times1.323129=$3969.39$.

Step3: Calculate the interest earned

The interest earned $I=A - P$. $I=3969.39 - 3000=$969.39$.

Answer:

A. The amount of money in the account after 4 years is $$3969.39$. B. The interest earned is $$969.39$.