# HIRE PURCHASE AND INSTALLMENT BUYING EXERCISE 2.3.5

1.A wash machine costs 10,200 cash down. It was bought by paying a down payment of 2,000 and the balance was agreed to be paid in 6 equal monthly installments of 1,500 each find the rate of interest.

Solution:

Cost price = 10,200.00
Down payment = 2,000.00
Balance = 10,200.00 – 2,000.00 = 8,200.00

Number of installments = 6
Amount of each installment (I) = 1,500.00
Amount paid in 6 installments (n)= 1,500 x 6 = 9,000.00
Excess amount paid = 9,000 – 8,200 = 800.00

Rate of interest = 2400E /n[(n + 1 )I – 2E]

= (2400×800)/6[(6 + 1) 1500 – 2×800]

= 2400×800/6(7×1500 – 1600)

= (2400×800) /6(10500 – 1600)

= 2400 x 800/6×8900 = 35.95%

1. The cost of an android mobile phone is 8,990. Joseph bought it by paying 500 Cash down and the balance he agreed to pay in 10 monthly installments of 900 each. Nizam bought the same phone by initially paying 900 and the Remaining balance is 8 installments of 1,200 each. Who has paid more rate of interest?

Solution:

Cost price of the phone = 8,990.00

(i) cash down payment

Paid by Joseph = 500

Balance = 8,990.00 – 500.00 = 8,490.00

Number of installments (n) =10

Amount of each installments (i) = 900.00

Amount paid in installments = 900×10 = 9,000.00

Extra amount paid = 9000 – 8490 = 510

Rate of interest = 2400E/N[(n+1)l – 2E]

= 2400 x 510/10[(10+1)900 – 2x 510]

= 2400 x 510/10[11 x 900 – 2 x 510]

= 2400 x 510/10 x 880

= 13. 78%

(ii) Cash down payment

made by Nizam = 900.00

Balance = 8,990.00 – 900.00 = 8090.00

Number of installments(n) = 8

Amount of each installments(i) = 1,200.00

Amount paid in installments = 1,200 x 8 = 9,600.00

Extra amount paid(E) = 9,600.00 – 8,090.00 = 1,510.00

Rate of interest = 2400E/N[(n+1)I – 2E]

= 2400×1510/8(10,800 – 3,020)

= 2400×1510/ 8×7780

= 58.226%

Nizam is paying a higher rate of interest.

1. The cost of a motor bike is 48,000.The company offers it in 30 months of Equal Installments at 10% rate of interest. Find the equated monthly installment.

Solution:

R = 48,000.00 R = 10%

N= 30(number of installments)

Monthly installment I = P(2nR+2400) /N[2,400+(n+1)R]

= 48,000(2x30x10+2,400)/30[2,400+(30-1)10]

= 48,000(600+2,400)/30(2,400+290)

= 48,000×3,000/30×2690 = 48,00,000/2690 = 4,80,000/2690

= 480000/269

= 1784.38

1. The cost of a set of home appliances is 36,000. Siri wants to buy them under a scheme of 0% interest and by paying 3 EMI in advance. The firm charges 3% as processing charges. Find the EMI and the installment for a period of 24 months.

Solution:

Cost of the set of home appliances (P) = 36,000.00

Number of installments (n) = 24

Amount of each installment = P/n = 36,000/24 = 1,500.00

Amount paid in advance = SEMI = 1500 x 3 = 4,500.00

Processing charge at the rate of 3% = 36,000 x 3/100  = 1,080.00

The total amount paid = 1,500 x 24+1,080

= 36,000+1,080

= 37080

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