Question

1. janila deposits $800 in an account that earns yearly simple interest at a rate of 2.65%. how much money is in the account after 3 years and 9 months? show your work.

solution

1. carmela borrows $400 and will pay 5.25% yearly simple interest. how much more interest will carmela owe if she borrows the money for 4 years instead of 2 years? show your work.

solution

1. ellie borrows money at a yearly simple interest rate of $6\frac{1}{2}$%. after 4 years, ellie owes $39 in interest. how much money did ellie borrow? show your work.

solution

1. lilia borrows $400 at a yearly simple interest rate of 6%. she writes the expression $400+(0.6×400)$ to represent the total amount of money she will pay back for borrowing the money for 1 year. is lilias expression correct? explain your answer and determine the amount of money lilia will need to pay back after 1 year.

Explanation:

(Question 3):

Step1: Convert time to years

3 years 9 months = $3 + \frac{9}{12} = 3.75$ years

Step2: List given values

Principal $P = \$800$, Rate $r = 2.65\% = 0.0265$, Time $t = 3.75$

Step3: Calculate simple interest

$I = P \times r \times t = 800 \times 0.0265 \times 3.75$
$I = 800 \times 0.099375 = 79.5$

Step4: Find total account value

Total = $P + I = 800 + 79.5$

(Question 4):

Step1: Calculate interest for 4 years

$I_1 = 400 \times 0.0525 \times 4 = 84$

Step2: Calculate interest for 2 years

$I_2 = 400 \times 0.0525 \times 2 = 42$

Step3: Find difference in interest

$\text{Extra Interest} = I_1 - I_2$

(Question 5):

Step1: Convert rate to decimal

$6\frac{1}{2}\% = 6.5\% = 0.065$

Step2: Rearrange simple interest formula

$P = \frac{I}{r \times t}$, where $I=39, r=0.065, t=4$

Step3: Solve for principal

$P = \frac{39}{0.065 \times 4} = \frac{39}{0.26}$

(Question 6):

Step1: Check rate conversion

6% = 0.06, not 0.6. Lilia used 0.6 incorrectly.

Step2: Calculate correct total amount

Total = $400 + (0.06 \times 400) = 400 + 24$

Answer:

(Question 3):
$\$879.50$

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