6.1 homework simple and compound interest (31 pts)\nscore: 5/20 answered: 6/11\nquestion 5\nlynne needs to…

6.1 homework simple and compound interest (31 pts)\nscore: 5/20 answered: 6/11\nquestion 5\nlynne needs to borrow $9500 for cosmetic surgery. she obtains a loan from her grandmother for 54 months at a simple interest rate of 9.5%. what is the loans future value?\nquestion help: video\nsubmit question

6.1 homework simple and compound interest (31 pts)\nscore: 5/20 answered: 6/11\nquestion 5\nlynne needs to borrow $9500 for cosmetic surgery. she obtains a loan from her grandmother for 54 months at a simple interest rate of 9.5%. what is the loans future value?\nquestion help: video\nsubmit question

Answer

Explanation:

Step1: Convert time to years

The time $t$ is 54 months. Since 1 year has 12 months, $t=\frac{54}{12}= 4.5$ years.

Step2: Identify the principal and interest - rate

The principal amount $P = 9500$, and the simple - interest rate $r=9.5%=0.095$.

Step3: Use the simple - interest formula for future value

The formula for the future value $A$ of a simple - interest loan is $A = P(1 + rt)$. Substitute $P = 9500$, $r = 0.095$, and $t = 4.5$ into the formula: [ \begin{align*} A&=9500\times(1+0.095\times4.5)\ &=9500\times(1 + 0.4275)\ &=9500\times1.4275\ &=13551.25 \end{align*} ]

Answer:

$13551.25$