Mathematics, 31.10.2019 01:31 ashiteru123

You borrow $5,000 from your parents to purchase a used car. the arrangements of the loan are such that you make payments of $250 per month toward the balance plus 1% interest on the unpaid balance from the previous month. (a) find the first year’s monthly payments and the unpaid balance after each month. (b) find the total amount of interest paid over the term of the loan.

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Answer from: juana2019

Part A:
1st month: Interest payable = 1% of $5,000 = $50.00
Amount paid in first month = $250 + $50.00 = $300
Unpaid balance = $5,000 - $250 = $4,750

2nd month: Interest payable = 1% of $4,750 = $47.50
Amount paid in second month = $250 + $47.50 = $297.50
Unpaid balance = $4,750 - $250 = $4,500

3rd month: Interest payable = 1% of $4,500 = $45.00
Amount paid in third month = $250 + $45.00 = $295.00
Unpaid balance = $4,500 - $250 = $4,250

4th month: Interest payable = 1% of $4,250 = $42.50
Amount paid in fouth month = $250 + $42.50 = $292.50
Unpaid balance = $4,250 - $250 = $4,000

5th month: Interest payable = 1% of $4,000 = $40.00
Amount paid in fifth month = $250 + $40.00 = $290.00
Unpaid balance = $4,000 - $250 = $3,750

6th month: Interest payable = 1% of $3,750 = $37.50
Amount paid in sixth month = $250 + $37.50 = $287.50
Unpaid balance = $3,750 - $250 = $3,500

7th month: Interest payable = 1% of $3,500 = $35.00
Amount paid in seventh month = $250 + $35.00 = $285.00
Unpaid balance = $3,500 - $250 = $3,250

8th month: Interest payable = 1% of $3,250 = $32.50
Amount paid in eighth month = $250 + $32.50 = $282.50
Unpaid balance = $3,250 - $250 = $3,000

9th month: Interest payable = 1% of $3,000 = $30.00
Amount paid in ninth month = $250 + $30.00 = $280.00
Unpaid balance = $3,000 - $250 = $2,750

10th month: Interest payable = 1% of $2,750 = $27.50
Amount paid in fouth month = $250 + $27.50 = $277.50
Unpaid balance = $2,750 - $250 = $2,500

11th month: Interest payable = 1% of $2,500 = $25.00
Amount paid in seventh month = $250 + $25.00 = $275.00
Unpaid balance = $2,500 - $250 = $2,250

12th month: Interest payable = 1% of $2,250 = $22.50
Amount paid in eighth month = $250 + $22.50 = $272.50
Unpaid balance = $2,250 - $250 = $2,000

Part B:
Number of payments = 5000 / 250 = 20
Total amount of interest = 50 + 47.5 + 45 + . . . + upto the 20th payment.
This is an arithmetic sequence with the first term as 50, common difference as -2.5 and number of terms = 20.

Sum of the first 20th term of the GP is given by
$S_n= \frac{20}{2}[2(50)+(20-1)(-2.5)] \\ \\ =10(100-2.5(19))=10(100-47.5) \\ \\ =10(52.5)=\$525.00$

Therefore, the total amount of interest paid over the term of the loan is $525.00

Answer from: Quest

c. x=2.4cm

step-by-step explanation:

similar triangles are triangles which have the same shape but not the same size. this means their angle measures are equal but their side lengths are not instead they are proportional. to solve, we will set up a proportion and solve.

a proportion is two equal ratios set equal to each other. we form the ratios by finding corresponding sides (sides which match to each other on both triangles by their position). out ratios will be one side of the small triangle over the corresponding side on the big triangle as shown below:

$\frac{little}{big} =\frac{side mn}{side ab}=\frac{side on}{side cb}$ .

$\frac{0.96}{1.2}=\frac{x}{3}$

to solve the proportion, we'll cross multiply by multiplying numerator with denominator across the equal sign.

$0.96(3)=1.2(x)\\2.88=1.2x\\\frac{2.88}{1.2}=\frac{1.2x}{1.2} \\2.4=x$

Answer from: Quest

answer: 204

step-by-step explanation:

we are told that the revenue is

x⋅(4080−10x)=−10x^2+4080x

this is a quadratic function, so to maximize it we should find the x-value of its vertex. recall that the x-value of the vertex of the parabola ax^2+bx+c is given by the formula −b/2a.

so in this case, we have a=−10 and b=4080, so the x-value of the vertex is

−b/2a= −(4080)/2(−10)=204

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