You have a part time job in your junior year of high school. You need to borrow $2,000 to purchase a used car to drive to work. The local bank will lend you money for 2 years at a rate of 9% compounded quarterly. Your uncle offers to lend you the money in the form of a promissory note for 2 years with an annual simple interest rate of 6%. How much money will you save by borrowing the money from your uncle?

$149.66

Step-by-step explanation:

Step 1

Calculate Total Amount payable to the bank using compound interest

Total Amount payable (A) =

P(1 + r/n)^nt

P = Principal = $2000

r = Interest rate = 9% = 0.09

n = compounding interest = quarterly = 4

t = time in years = 2

Total Amount payable

= 2000(1 + 0.09/4)^0.09 × 2

A = $ 2,389.66

Interest = A - Principal

= $ 2,389.66 - $ 2,000.00

I (interest) = $ 389.66

Step 2

Calculate the Total amount payable to his uncle using simple interest.

Total Amount (A) = P(1 + rt)

P = Principal = $2000

r = Interest rate = 6% = 0.06

t = time in years = 2

A = 2000(1 + 0.06 × 2)

A = $2,240

A - Principal

= $ 2,240 - $ 2,000.

I (interest) = $240

Step 3

The amount of money you will save by borrowing the money from your uncle is calculated as:

Amount payable to the bank - Amount payable to your uncle

= $ 2,389.66 - $2,240

= $149.66

Therefore, the amount of money you will save by borrowing the money from your uncle is $149.66

the system of inequalities is

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

the equation of the dashed line is

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

the equation of the solid line is

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

step 3

the system of inequalities is

step-by-step explanation: