**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%

**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.

**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**

**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**

Pingback: IX – Table of Contents – Breath Math