Question

lesson 20 | session 2
3 jamila 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
4 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
5 ellie borrows money at a yearly simple interest rate of 6½%. after 4 years, ellie owes $39 in interest. how much money did ellie borrow? show your work.
solution
6 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 lilia’s expression correct? explain your answer and determine the amount of money lilia will need to pay back after 1 year.

Explanation:

Problem 3

Step1: Recall simple interest formula

The formula for simple interest is \( I = P \times r \times t \), where \( P \) is the principal amount, \( r \) is the annual interest rate (in decimal), and \( t \) is the time in years. The total amount \( A \) in the account is \( A = P + I \).

First, convert the time to years. 3 years and 9 months: 9 months is \( \frac{9}{12} = 0.75 \) years, so \( t = 3 + 0.75 = 3.75 \) years.

The principal \( P = 800 \) dollars, the rate \( r = 2.65\% = 0.0265 \).

Step2: Calculate the interest

Using the simple interest formula \( I = P \times r \times t \), substitute the values:
\( I = 800 \times 0.0265 \times 3.75 \)
First, calculate \( 800 \times 0.0265 = 21.2 \)
Then, \( 21.2 \times 3.75 = 79.5 \)

Step3: Calculate the total amount

The total amount \( A = P + I = 800 + 79.5 = 879.5 \)

Step1: Recall simple interest formula

The formula for simple interest is \( I = P \times r \times t \), where \( P \) is the principal, \( r \) is the rate (in decimal), and \( t \) is time in years.

First, convert the rate to decimal: \( 5.25\% = 0.0525 \), principal \( P = 400 \) dollars.

Step2: Calculate interest for 4 years and 2 years

For \( t = 4 \) years: \( I_4 = 400 \times 0.0525 \times 4 \)
\( I_4 = 400 \times 0.21 = 84 \)

For \( t = 2 \) years: \( I_2 = 400 \times 0.0525 \times 2 \)
\( I_2 = 400 \times 0.105 = 42 \)

Step3: Find the difference in interest

The difference \( \Delta I = I_4 - I_2 = 84 - 42 = 42 \)

Step1: Recall simple interest formula

The formula for simple interest is \( I = P \times r \times t \), where \( I \) is interest, \( P \) is principal (the amount borrowed), \( r \) is rate (in decimal), and \( t \) is time in years. We need to solve for \( P \).

First, convert the rate to decimal: \( 6\frac{1}{2}\% = 6.5\% = 0.065 \), \( I = 39 \) dollars, \( t = 4 \) years.

Step2: Rearrange the formula to solve for \( P \)

From \( I = P \times r \times t \), we can solve for \( P \) by dividing both sides by \( r \times t \):
\( P = \frac{I}{r \times t} \)

Step3: Substitute the values and calculate

Substitute \( I = 39 \), \( r = 0.065 \), \( t = 4 \):
\( P = \frac{39}{0.065 \times 4} \)
First, calculate the denominator: \( 0.065 \times 4 = 0.26 \)
Then, \( P = \frac{39}{0.26} = 150 \)

Answer:

The amount of money in the account after 3 years and 9 months is \(\$879.50\).

Problem 4