Question

A man repays a loan of rs 65000 by paying rs400 in the first month and then increasing the payment by rs 300 every month. How long will it take for him to clear the loan?​

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Answer 1

Answer:

20 months

Step-by-step explanation:

Given  

 A man repays a loan of rs 65000 by paying rs 400 in the first month and then increasing the payment by rs 300 every month. How long will it take for him to clear the loan?​  

Let the loan be cleared in n months.

Now the amount is in A.P .

Let the first payment be 400

So second will be 400 + 300  

Third will be 400 + 300 + 300 and so on.

So S = 400 + 700 + 1000 +….and so on.

a = 400. d = 300

Now sum to n terms is given by

Sn = [n/2 (2 a + (n – 1) d]

65,000 = [n/2 (800 + (n – 1)300]

1,30,000 = 500 n + 300 n^2

300 n^2 + 500 n – 1,30,000 = 0

We can use n = - b ± √b^2 – 4 a c

                          --------------------------

                                    2 a

                 n = - 500 ±√250000 + 15,60,00000 / 600  

                  n = - 500 ± 12,500 / 600

                  n = 20

 Thus the loan will be cleared in 20 months.

Answer 2

Answer:

It takes 20 months for the man to repay the loan if he starts by paying 400 and increases the amount by 300 each month.

Step-by-step explanation:

Step 1 : This is an Arithmetic progression.

The sum of an Arithmetic progression is given by :

Sn = n/2 [2a + (n - 1) d]

Where :

Sn = The sum (total amount to be paid)

n = The number of terms.(number of months taken to clear the payment )

a = The first term (The first amount to be paid)

d = The common difference.(The amount by which the payment increases)

Step 2 : Identify the given values in the question.

Sn = 65000

d = 300

a = 400

Step 3 : Do the substitution.

65000 = n/2 [2 × 400 + (n - 1) 300]

65000 = n/2[ 800 + 300n - 300]

65000 = 400n + 150n² - 150n

65000 = 150n² + 400n - 150 n

65000 = 150n² + 250n

150n² + 250n - 65000 = 0

Divide through by 50:

3n² + 5n - 1300 = 0

Now solve for n.

The roots are - 60 and 65

We expand the equation below :

3n²- 60n + 65n - 1300 = 0

3n(n - 20) + 65(n - 20) = 0

(3n + 65)(n - 20) = 0

3n = - 65

n = - 65/3

n = 20

n = - 65/3 or 20

Since n is an integer and a positive number, we will take 20.

It therefore takes 20 months to clear the payment.