Quantitative Aptitude Compound Interest Study Material
1. We have learnt earlier that if Principal = Rs. P, Rate= R% per annum and Time=T years then the simple interest is given by the formula
Clearly, when money is borrowed on simple interest then the interest is calculated uniformly on the original principal throughout the loan period.
However, in post offices, banks, insurance corporations and the other money lending and deposit taking companies, the method of calculating interest is quite different.
Under this method, the borrower and the lender agree to fix up a certain unit of-time say yearly or half-yearly or quarterly, to settle the previous account.
In such cases, the interest accured during the first unit of time is added to the original principal and the amount so obtained is taken as the Principal for the second unit of time.’ The Amount of this Principal at the end of second unit of time becomes the Principal for the third unit of time and so on.
After a certain specified period, the difference between the Amount and the money borrowed is called (he Compound Interest (C.I.) for that period. ,
2. The fixed unit of time is known as the conversion period.
3. Let us take an example to explain the process. Let us suppose Rs. 1000 is lent for 2 years at 10%
Obviously, . . .
S.I = 1000 x 2×10/ 100 = Rs.200
Hence, amount after 2 years under S.I.
= Rs. 1000 +Rs. 200 = Rs. 1200.
Now, interest on Rs. 1000 at 10% after 1 year.
1000x10x1 /100 = Rs.100
Under C.I. this interest will be added to the original principal i.e. Rs. 1000 so that the amount after 1 year = Rs. 1000 + Rs. 100. i.e. Rs. 1100. This amount becomes the principal for the 2nd year. Now, interest on Rs. 1100 at 10% for 1 year
1100x10x1/100 = Rs.110
Hence, amount after 2 years = Rs. 1100+Rs. 110 = Rs. 1210.
It is the final amount.
.•. C.I. = Final amount – Original amount = Rs.(1210-1000) = Rs.210.
(i) If P is the original Principal, R is the rate of interest per annum, T is the number of years, for which the money is lent and A is the final amount, then
(ii) If the interest is payable half-yearly, then time is multiplied by 2 and the rate is.halved.
(iii) If the interest is payable quarterly, then time is multiplied by 4 and the rate is divided by 4.
(iv) When interest is compounded annually but time is infraction say 5 (2/3) years then
(v) When rates are different for different years, say R, %. R2%, R3% for 1st, 2nd and 3rd year respectively.
7. If the difference between SI and Cl on a certain sum of money for 2 years at R% per annum is D. Then the sum
8. If the difference between SI and Cl for a certain sum of money for 3 years at R% per annum is D. Then the sum
9. If a sum ‘A’ becomes ‘B’ in T1 years at compound rate of interest, then after T2 years the sum becomes
10. The compound interest is calculated annually in general unless some other period is clearly otherwise stated.
11. The compound interest is always greater than the simple interest for the same period and at the same rate. However, the C.I. for one year is equal to the S.I. for one year if calculated annually.