Simple and Compound Interest

(S.I. for two years = Rs. 10,000 X 2 X 10 = Rs. 2000  100 Interest for first year = Rs. 10000 X 1 X 10 = Rs.1000   100 Interest for second year = Rs. 1000 + 10% of Rs. 1000 = Rs. 1100 Total interest for 2 years (C.I.) = Rs. 2100 Difference = Rs. 100)

(No interest is earned on Rs. 840 since it is the simple interest, i. e. simple interest remains the same. Hence no change.)

In compounding, interest is added to the principal at the end of each period. This new total becomes the principal for the next period, meaning the amount on which interest is calculated increases over time.

Compounding frequency affects the total interest earned. More frequent compounding (e.g., quarterly vs. yearly) results in a higher effective interest rate and thus more total interest.

Total amount due = Rs. 20, 000             Paid in cash = Rs. 8, 000             Balance = Rs. 12, 000             Interest = 12,000*18%*2/12 = Rs. 360             Amount of bill = 12000 + 360= Rs. 12, 360 If the new bill is for 3 months, then its amount will be Rs. 12, 540 If the new bill is 8000 + Interest, then its amount will be Rs. 8,240 for 2 months bill and Rs. 8,360 for 3 months bill.

Time = ( 24 + 31 + 18 ) days = 73 days = 73/365 year = 1/5 year P = 3000, R = 25/4 % p.a S.I = ( 3000 ´ 25/4 ´ 1/5 ´ 1/100 ) = 37.50

Let sum = Rs x . Then, simple interest = 4x / 9 Let rate = R% & time = R years
Then, (x ´ R ´ R ) / 100 = 4x / 9, R² = 400/9, R = 20/3 Rate = 20/3% & time = 20/3 years

Principal = Rs ( 100 ´ 5400 ) / 12 ´ 3 = 15000

Let sum = x, then, simple interest = x/2

Simple interest = ( 956 - 800 ) = 156, Rate = ( 100 ´ 156 ) / 800 ´ 3 % = 13/2 % New Rate = ( 13/2 + 4 )% = 21/2 % New SI = ( 800 ´ 21/2 ´ 3/100 ) = 252 Therefore new amount = ( 800 + 252 ) = 1052

Principal = Rs. 8000, Amount = Rs. 9261 Rate = 5% per annumLet the time be n years, Then , 9261 = 8000 (1+r/100)n => 9261/8000 = (1+5/100)n = (21/20)n => 441/400 = (21/20)n => (21/20)3 = (21/20)n => n = 3 years

Time = Interest x 100             Principal x Rate Thus, 15925 x 100            70,000 x 6.5 i.e. 3.5 years

The interest will be charged on balance of Rs. 6,000 to be paid later. Interest = 6000 x 18/100 x 3/12 = Rs. 270

Interest = 50,000 * 5.5*2 /100 = Rs. 5500 Interest = 5500 Amount = 50000 + 5500 = Rs. 55,500

The present value at 8% p.a. for 15 years from the standard table is 8.5525 which multiplied by 15,000 amounts to Rs. 1,28,288 approx.