8) jose wants to save money for a house and finds two accounts that pay 3% in interest. he wants to invest…

8) jose wants to save money for a house and finds two accounts that pay 3% in interest. he wants to invest $3000. he has 2 options to invest his money. option a is a simple interest account with a time period of 10 years. option b is a compound interest account with a time period of 12 years. what would be his account balance in option b? $1,277.28 $4,277.28 $900 $1,080

8) jose wants to save money for a house and finds two accounts that pay 3% in interest. he wants to invest $3000. he has 2 options to invest his money. option a is a simple interest account with a time period of 10 years. option b is a compound interest account with a time period of 12 years. what would be his account balance in option b? $1,277.28 $4,277.28 $900 $1,080

Answer

Explanation:

Step1: Identify compound - interest formula

The compound - interest formula is $A = P(1 + r)^t$, where $P$ 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 $t = 12$ years.

Step3: Substitute values into the formula

$A=3000\times(1 + 0.03)^{12}$. First, calculate $(1 + 0.03)^{12}$. Using a calculator, $(1.03)^{12}\approx1.42576$. Then, $A = 3000\times1.42576=$4277.28$.

Answer:

$4277.28$