INSTALMENTS

ALGORITHM

STEP.1 Obtain Cash price (CP) of the article.

Step. 2  Obtain cash down payment (DP).

Step 3.  Compute balance due (BD) by using

      BD = CP - DP

Step 4.  Obtain the given quantities, e.g.

    P= Value of each installment

    n= Number of installments.

    R= Rate of interest. etc.,

Step 5.  Assume the unknown quantity and use the following formula to compute it.

 (1+ nR/1200) BD= {1+ (n-1)R/2400} nP.

Remark: Sometimes in an installment buying plan the balance due is paid in just one installment after a certain number of months (say n). In such cases,  we have 

   Amount of the balance due= Volume of the installment.

=> BD + (BD x R x n)/1200= value of the installment.

=> (1+ nR/1200)BD = Value of the Installment.

EXERCISE- 1

1) A briefcase is available for Rs 1600 cash or for ₹600 cash down payment and ₹1080 to be paid after 6 months. Find the rate of interest charged under the installment plan.                         16%

2) A room heater is sold for ₹440 Cash for ₹200 cash down payment together with ₹244 to be paid after 1 month. Find the rate of interest charged in the installment scheme.                     20%

3) One can purchase a room cooler for ₹2400 cash or for ₹1200 Cash down payment and two monthly installments of ₹610 each. Find the rate of interest charged under the installment plan.   13.40%

4) A scooter can be purchased for ₹2800 Cash or for ₹7400 cash down payment followed by 4 equal monthly installments ₹5200 each. Find the rate of interest charged under the installment plan.   4.69%

5) A tractor is sold for ₹450000 Cash or for ₹150000 cash down payment together with 10 equal installments of ₹32000 each . Find the rate of interest charged under the installment plan.   15.38%

6) An electric generator is sold for ₹39000 cash or for 25% cash down payment and 8 equal monthly installments of ₹3900 each. Calculate the rate of interest charged.      18.75%

7) A videocamera can be purchased for ₹60000 cash or for 20% cash down payment and ₹48000 in equal monthly installments of ₹5000 each. What rate of interest does the buyer pay ?    9.41%

8) A Xerox machine is available for ₹78000 cash or for ₹ 100/3% cash down payment and 11 equal monthly installments of ₹4900 each . Calculate the rate of interest charged .    7.54%

9) A ceiling fan is marked at ₹970 cash or for ₹210 Cash down payment followed by 3 equal monthly Installments. If the rate of interest charged under the installment plan is 16% per annum, find the monthly installment.                       ₹260

10) A computer is sold by a company for ₹19200 cash or for ₹4800 cash down payment together with 5 equal monthly installments. If the rate of interest charged by the company is 12% per annum, find each installment.   ₹2964.70

11) An article is available for ₹7000 cash for ₹1900 cash down payment and 6 equal monthly installments. If the rate of interest charged is 5/2% per month, determine each installment.     ₹920

12) A gas cooking range is available for ₹2500 cash or for ₹520 cash down payment followed by 4 equal monthly installments. If the rate of interest charged is 25% per annum, calculate the monthly installment.             ₹520

13) A bicycle is available for ₹150 cash payment or for ₹360 cash down payment and rest in equal monthly installments of ₹390 each. If the rate of interest charged 16%, find the number of Installments .  3

14) The cost of a washing machine is ₹9000. The buyer agrees to pay ₹2200 in cash and the balance in monthly equal installments of ₹1400 each . If the interest charged is at the rate of 12% per annum, find the number of Installments .    5

15) An article is available on cash down payment of ₹3260 and 9 equal monthly installments of ₹560 each. If the rate of interest charged is 16% per annum, find the price of the article.              ₹8000

16) An article is available for ₹250 cash down payment followed by ₹260 after 3 months. If the interest charged is  16% per annum, determine the cash price of the article.                                ₹500

17) A briefcase is available for ₹800 cash or for ₹500 cash down payment and ₹320 to be paid after six months. Find the rate of interest charged under the Installment plan.                      13.33%

18) An electric iron is available for ₹550 cash or for ₹250 cash down payment and ₹305 to be paid after two months. Find the rate of interest charged under the Installment plan.                   10%

19) A room cooler is available for ₹2000 cash or for ₹1000 cash down payment and ₹1040 to be paid after three months. Find the rate of interest charged under the Installment plan.                      16%

20) An article is sold for ₹500 cash or ₹150 cash down payment followed by 5 equal monthly installment. If the rate of interest charged is 18% per annum, compute the monthly installment.        73.06%

21) Romesh borrowed ₹6500 at 15% p.a simple interest. He paid it back in one year by twelve equal monthly installments. Find the value of each Installment.                                 ₹583

22) Simran borrowed ₹18000 to buy a TV and agree to pay ₹6000 in cash followed by a equal monthly installment. If she has to pay 10% p.a simple interest for the money borrowed, find the value of each installment.                ₹1387

23) A ceiling fan is sold for ₹485 or for ₹105 cash down payment and the rest in equal monthly installment of ₹130 each. If the rate of interest charged is 16% p.a. find the number of installment.     3

Present value : The present value of ₹A due n years later is the amount of money needed now so that if it is invested now at a certain rate of interest, the sum of ₹A can be obtained at the end of n years.

Present value of ₹A due n years later at the compound rate of interest R% per annum, it means that if we invest ₹P now for n years at R% per annum compounded annually, we will get ₹A at the end of n years.

So,

A= Amount of ₹ P after n years at the rate of R% per annum compounded annually.

=> A= P(1+ R/100)ⁿ 

=> P= A(1+ R/100)⁻ⁿ

Note:  If the intrest is R% per annum compounded half yearly, then the present value of ₹A payable after n years is given by

P= A(1+ R/200)⁻²ⁿ.

Similarly, the present value of ₹A due n years at R% per annum compounded quarterly is given by

P= A(1+ R/400)⁻⁴ⁿ

EXERCISE-2

1) Find the present value of ₹1210 due 2 years at 10% per annum compounded annually.                                           1000

2) Find the present value of ₹14045 due 1 year hence at 12% per annum, compounded half yearly.           ₹12500

The sum of the present values of Installments of an Installment scheme is known as the present value of all installments or present value of Installment scheme.

Present value of all Installments= 

100P/R {1- (1+ R/100)⁻ⁿ}

Note:

A) If the intrest is R% per annum compounded half yearly, then

Present value of n-instalments = 

200P/R {1- (1+ R/100)⁻ⁿ}

B) If the intrest is R% per annum compounded quarterly, then

Present value of n-instalments=

400P/R {1- (1+ R/100)⁻ⁿ}

Algorithm:

Step 1. Obtain the value of each installment, number of Installments and the rate of interest.

Step 2.  Assume  the unknown quantity.

Step 3.  Find the present value of all Installments by using the suitable formula given above.

Step 3. Obtain the sum borrowed.

Step 4. Equate the present value of all Installments to the sum borrowed to find the unknown quantity .

* Sum borrowed= Present value of all Installments.

* Total amount paid= Number of installment x Value of each installment.

* Intrest charged= Total amount as Installment - sum borrowed 

EXERCISE- 3

1) A loan has to be returned in two equal installments . If the rate of interest is 16% per annum compounded annually and each installment is of ₹1682,  find the sum borrowed and the total interest charged.                2700, 664

2) A person borrowed some money on compund intrest and returned it in 3 years in equals annual Installments. If the rate of interest is 15% in person program and on installment is 48016 find the summer out Ramba Road someone in return it in 3 equal quarterly installment of 17576 age find the summa aroad if the rate of interest charged was 16% for annum compounded quarterly find also the total interest money for a finance company and has to payback into two equal half yearly installment 4944 ecp the entrance recharge by the finance company at the rate of 15% per annum compounded semi only find the principal in the total interest paid state government announced sale of flat 550,000 cash for 42750 cash down payment 3 call installment the government also charge the nominal interested the rate of 8% per compound annual purchase a flat under this installment blon calculate the value of each installment TV set is available for rupees 19650 cash payment offer 3100 cash down payment and three equal in annual installment in the shopkeeper charges at the rate of 10% compounder is available for 39300 cash or 12 payment and three equal half yearly installment at the dealer charge interested 20% for mm compound seminarly calculate each installment builder Naam Se sale of flat for RS 30 lakh cash or for 10000 31600 cash down payment and 3 equal quarterly installment in the rate of interest at 10% and I'm bounded quarterly complete the value of each installment under the installment scheme also find the total interest Housing Society charges for flat 16000 ask for 58500 cash down payment and 3 equal half yearly installment is the society charges 16% for annum interest compounded half yearly calculate the value of each installment find also the total interest charged in how many unable instrument of 146 of Sun 390 200 can be paid back at the rate of interest is 4% per annum compounder and in how many annual installment rupees 4232 each a loan of 6880 can be paid back in the interest chapter 3 person compounded annually but annual payment will discharge attempt of 582 due into your 10% per annum compounder annually