A couple decides to buy a house which is currently valued at $318,921.46 on loan. The couple is willing to start paying $200.00 per month and are willing to increase their payment at a rate of 5% every month. How many payments are necessary to pay off the loan amount assuming no deposit was made (answer to the nearest whole number)? What is the value of the final payment that they would make assuming no deposit was made (answer to the nearest whole number)? [Hint: apply geometric sequences].

A.) 90 payments are necessary to pay off the loan amount assuming no deposit was made

B.) Final payment = 15377 dollars

Step-by-step explanation:

Given that the first payment = $200

Paying at 5% increase every month. That is, in the next month couple will pay 200 × 1.05 and the month after, they will pay  200 × 1.05^2

This sequnce of payments is geometric progression.This means that payment made at month number (n+1) is 

200 × 1.05^n

Sum of payments made in the first (n+1) month is equal to:

200 + 200 × 1.05 + 200 × 1.05^2 + ...+ 200 × 1.05^n

= 200 × (1 + 1.05 + 1.05^2 + ...+1.05^n)

= 200 × (1.05^{n+1}-1)/(1.05-1)

= 200/0.05 × (1.05^{n+1}-1)

= 4000 × (1.05^{n+1}-1

This sum should be equal or greater than the value of the house $318,921.46.

If n+1 = 89,

Sum of payments will be $303,544.25 which is not up to the value of the house

If n+1 = 90,

Sum of payments will be $318,921.460.

Therefore, 90 payments are necessary to pay off the loan amount assuming no deposit was made.

Assuming no deposit was made. Final payment will be 

200 × 1.05^{89} = 15377.212

= 15377 dollars ( approximately)

25/4

step-by-step explanation:

call segment cd's length x. because dc and ab are parallel, angle acd and cab, so triangles adc and abc are similar and we can set up the equation x / ac = ac / ab, or x / 5 = 5 / 4 and x = 25/4.

it is true

step-by-step explanation:

all the combinations add up i used   calculator