compound interest Topic-wise Practice Test, Examples With Solutions & More Shortcuts
compound interest & IT'S TYPES
Useful for Management (CAT, XAT, MAT, CMAT, IIFT, SNAP & other), Bank (PO & Clerk) SSC (CGL, 10+2, Steno, FCI, CPO, Multitasking), LIC (AAO & ADO) CLAT, RRB, UPSC and Other State PSC Exams
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compound interest Topic-wise Types, Definitions, Important fact & Techniques with Short Tricks & Tips useful for all competitive Examinations
Compound Interest - Basic Formulas, Shortcuts, Rules, Tricks & Tips - Quantitative Aptitude
Useful For All Competitive Exams Like UPSC, SSC, BANK & RAILWAY
Posted By Careericons Team
Introduction to Compound Interest:
The interest charged every year on the amount of the previous year is called compound interest. Money is said to be lent at compound interest when at the end of a fixed period, the interest that has become due and is not paid to the lender, but is added to the sum lent, and the amount thus obtained becomes the principal for the next period.
The process is repeated until the amount for the last period has been found. The difference between the original principal and the final amount is called compound interest. In simple interest borrowings, the principal remains constant through the period for which the sum is borrowed.
In borrowings at compound interest, the principal adds on the simple interest at the end of a year and becomes a new principal for the next year. The amount of interest accrued will also become different every year.
As the principal increases after every reckoning period, the amount of interest in Compound Interest will always be more than Simple Interest.
- The period at the end of which interest is compounded is called the conversion period. In the case of interest being compounded yearly, the number of conversions x is 1.
- Interest may also be compounded and added to the principal half-yearly, i.e., twice a year. In this case number of conversions per year is 2.
- If interest is compounded every three months, or quarterly, the number of conversions in a year is 4.
- If the interest is compounded every month, conversions number 12.
Unless the problem specifies, it is assumed that interest is compounded yearly or per annum. The more the number of conversions, the greater the value of C.I., other parameters remaining unchanged.
Basic Terms with Proper Definitions associatted with this topic Compound Interest:
| S. No | Term | Definition |
|---|---|---|
| 1 | Interest | It is the time value of money. It is the cost of using capital. |
| 2 | Principal | It is the borrowed amount. |
| 3 | Amount | It is the sum total of Interest and Principal. |
| 4 | Rate | It is the rate percent payable on the amount borrowed. |
| 5 | Period | It is the time for which the principal is borrowed. |
| 6 | Simple Interest | Simple Interest is payable on principal. |
| 7 | Compound Interest | Compound Interest is payable on Amount. |
Compounded Years Types & Its Formula For Compound Interest:
There are totally 6 Important Types of Formulas for solving all kinds of Compound Interest on which the Years are to be calculated in different specific periods of time and their sum amount. These six formulas will be very useful in solving aptitude problems asked based on this compound interest.
| S. No | Compounded Year | Sum Amount Formula |
|---|---|---|
| 1 | When interest compounded annually | Amount = $P [1 + r/{100}]^n$ |
| 2 | When interest compounded half yearly | Amount = $P [1 + {(r/2)}/{100}]^{2n}$ |
| 3 | When interest compounded quarterly | Amount = $P [1 + {(r/4)}/{100}]^{4n}$ |
| 4 | When interest compounded monthly | Amount = $P [1 + {(r/12)}/{100}]^{12n}$ |
| 5 | When time is in fraction of a year, say 3 $4/5$ years | Amount = $P [1 + r/{100}]^3 [1 + {(4/5r)}/{100}]$ |
| 6 | When rate of interest is $r_1$ % durring first year, $r_2$ % durring 2nd year, $r_3$ % durring 3rd year. | Amount = $P [1 + {r_1}/{100}] [1 + {r_2}/{100}] [1 + {r_3}/{100}]$ |
Note:
If Principal = Rs. P, Time = n years, Rate = r% per annum and interest compounded annually
"11" - Important Aptitude Rules, Formulas & Quick Tricks to Solve Compound Interest Based Aptitude Problems
In this list of rules, you will get an idea that How to solve all different types & kinds of Compound Interest based aptitude problems asked in various competitive exams like UPSC, SSC, Bank, and Railway examinations at all levels.
By using this method, you can able to solve all problems from basic level to advanced level of questions asked based on Compound Interest in a faster approch.
Let's discuss the rules one by one with all Compound Interest Rule & Formulas with examples,
RULE 1 :
If A = Amount, P = Principal, r = Rate of Compound Interest (C.I.), n = no. of years then,
A = P$(1 + r/100)^n$, C.I. = A - P
C.I. = P$[(1 + r/100)^n - 1]$
RULE 2 :
Compound interest is calculated on four basis:
| Term | Rate | Time(n) |
|---|---|---|
| Annually | r% | t years |
| Half–yearly (Semi-annually) |
$r/2$% | t × 2 years |
| Quarterly | $r/4$% | t × 4 years |
| Monthly | $r/12$% | t × 12 years |
RULE 3 :
If there are distinct 'rates of interest' for distinct time periods i.e.,
Rate for 1st year → $r_1$%
Rate for 2nd year → $r_2$%
Rate for 3rd year → $r_3$% and so on
Then, A = P$(1 + r_1/100)(1 + r_2/100)(1 + r_3/100)$...
C.I. = A – P
RULE 4 :
If the time is in fractional form i.e.,t = nF, then
A = P$(1 + r/100)^n(1 + {rF}/100)$e.g. t =3$5/7$ yrs,
then A = P$(1 + r/100)^3(1 + r/100 × 5/7)$
RULE 5 :
A certain sum becomes 'm' times of itself in 't' years on compound interest then the time it will take to become mn times of itself is t × n years.
RULE 6 :
The difference between C.I. and S.I. on a sum 'P' in 2 years at the rate of R% rate of compound interest will be
C.I – S.I. = P$(R/100)^2 = {S.I. × R}/200$
For 3 years, C.I. – S.I. = P$(R/100)^2 × (3 + R/100)$
RULE 7 :
If on compound interest, a sum becomes Rs.A in 'a' years and Rs.B in 'b' years then,
(i) If b – a = 1, then, R% = $(B/A - 1)$ × 100%
(ii) If b – a = 2, then, R% = $(√{B/A} - 1)$ × 100%
(iii) If b – a = n then, R% = $[(B/A)^{1/n} - 1]$ × 100%
where n is a whole number.
RULE 8 :
If a sum becomes 'n' times of itself in 't' years on compound interest, then
R% = $[n^{1/t} - 1] × 100%$
RULE 9 :
If a sum 'P' is borrowed at r% annual compound interest which is to be paid in 'n' equal annual installments including interest, then
(i) For n = 2, Each annual installment
= $p/{(100/{100 + r}) + (100/{100 + r})^2$
(ii) For n = 3, Each annual installment
= $p/{(100/{100 + r}) + (100/{100 + r})^2 + (100/{100 + r})^3$
RULE 10 :
The simple interest for a certain sum for 2 years at an annual rate interest R% is S.I., then
C.I. = S.I.$(1 + R/200)$
RULE 11 :
A certain sum at C.I. becomes x times in $n_1$ year and y times in $n_2$ years then
$x^{1/n_1} = y^{1/n_2}$
6 - Types of Compound Interest Based Aptitude Questions and Answers Practise Test With Online Quiz
Click the below links & Learn the specific model from Compound Interest problems that you have to practice for upcoming examination
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