Loan 5

Abdul takes a loan of 200000 from Ali and agrees to repay in number of instalment, each instalment begin with the 2nd exceeding the previous one by 1000, if the first instalment is 500, find how many instalment will be necessary to be wipe out
the loan? Completely

Correct answer:

n =  20

Step-by-step explanation:

$$\begin{gathered} a=200000 \\ {a}_1=500 \\ d=1000 \\ a={\displaystyle \frac{a_1+a_n}{2}}n \\ a={\displaystyle \frac{a_1+a_1+(n-1)\cdot d}{2}}\cdot n \\ 200000\ast 2=(500\ast 2+(n-1)\ast 1000)\ast n \\ 200000\cdot 2=(500\cdot 2+(n-1)\cdot 1000)\cdot n \\ -1000n^2+400000=0 \\ 1000n^2-400000=0 \\ a=1000;b=0;c=-400000 \\ D=b^2-4ac=0^2-4\cdot 1000\cdot (-400000)=1600000000 \\ D>0 \\ {n}_{1,2}={\displaystyle \frac{-b\pm \sqrt{D}}{2a}}={\displaystyle \frac{\pm \sqrt{1600000000}}{2000}} \\ {n}_{1,2}={\displaystyle \frac{\pm 40000}{2000}} \\ {n}_{1,2}=\pm 20 \\ {n}_1=20 \\ {n}_2=-20 \\ \text{ Factored form of the equation: } \\ 1000(n-20)(n+20)=0 \\ n=n_1=20 \end{gathered}$$

Our quadratic equation calculator calculates it.

Try another example

Related math problems and questions:

• Loans, loan ...
  In Slovakia, launched a short-term non-bank loans, of which few people have their "take" are considered unfavorable. Often, the borrower ends up in a spiral of debt, which takes more and more onerous loan used to repay earlier loans. Calculate how many 9-
• Repay, interest, loan
  Ramchacha takes a loan amount of 240000 from a bank for constructing a house at the rate of simple interest of 12% per annum. After 1 yr. of taking the loan he rents the house at the rate of 5200 per month. Determine the number of years he would take to r
• Three members GP
  The sum of three numbers in GP (geometric progression) is 21 and the sum of their squares is 189. Find the numbers.
• Loan
  Apply for a $ 59000 loan, the loan repayment period is 8 years, the interest rate 7%. How much should I pay for every month (or every year if paid yearly). Example is for practise geometric progression and/or periodic payment for an annuity.
• Sum 1-6
  Find the sum of the geometric progression 3, 15, 75,… to six terms.
• Geometric progression
  In geometric progression, a1 = 7, q = 5. Find the condition for n to sum first n members is: sn≤217.
• Find the sum
  Find the sum of all natural numbers from 1 and 100, which are divisible by 2 or 5
• Mortage hypo loan
  The Jonáš family decided to buy an older apartment, which cost EUR 30,000. They found EUR 17,000 and took the loan with the bank for the remaining amount. What interest did they receive if they repay this amount for 15 years at EUR 120 per month?
• Geometric seq
  Find the third member of geometric progression if a1 + a2 = 36 and a1 + a3 = 90. Calculate its quotient.
• Geometric progressiob
  If the sum of four consective terms of geometric progression is 80 and arithmetic mean of second and fourth term is 30 then find terms?
• Probably member
  Look at the series 2,6,25,96,285, ? What number should come next?
• Insert into GP
  Between numbers 5 and 640, insert as many numbers to form geometric progression so the sum of the numbers you entered will be 630. How many numbers must you insert?
• Bonuses
  Five employees of the company were paid bonuses so that each successor received 550 USD less than the previous employee. How much did everyone get if a total of USD 11,000 has paid?
• Present value
  A bank loans a family $90,000 at 4.5% annual interest rate to purchase a house. The family agrees to pay the loan off by making monthly payments over a 15 year period. How much should the monthly payment be in order to pay off the debt in 15 years?
• The sum
  The sum of the squares of two immediately following natural numbers is 1201. Find these numbers.
• Sum of odd numbers
  Find the sum of all odd integers from 13 to 781.
• Find x 2
  Find x, y, and z such that x³+y³+z³=k, for each k from 1 to 100. Write down the number of solutions.