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. click the icon to view some finance formulas. a. the amount of money in the account after 3 years is $ (round to the nearest hundredth as needed.) principal rate compounded time $3000 3% annually 3 years

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. click the icon to view some finance formulas. a. the amount of money in the account after 3 years is $ (round to the nearest hundredth as needed.) principal rate compounded time $3000 3% annually 3 years

Answer

Answer:

A. $3278.18 B. $278.18

Explanation:

Step1: Identify compound - interest formula

The compound - interest formula is $A = P(1 + r)^t$, where $A$ is the amount of money in the account after $t$ years, $P$ is the principal amount, $r$ is the annual interest rate (in decimal form), and $t$ is the number of years.

Step2: Convert the interest rate to decimal

Given $r = 3%=0.03$, $P=$3000$, and $t = 3$ years.

Step3: Calculate the amount $A$

Substitute the values into the formula: $A=3000\times(1 + 0.03)^3$. First, calculate $(1 + 0.03)^3=(1.03)^3=1.03\times1.03\times1.03 = 1.092727$. Then, $A = 3000\times1.092727=$3278.181\approx$3278.18$.

Step4: Calculate the interest earned

The interest earned $I$ is given by $I=A - P$. Substitute $A = 3278.18$ and $P = 3000$ into the formula. So, $I=3278.18-3000=$278.18$.