Formulas for Simple Interest And Compound Interest
July 12, 2023
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On this page we have discussed Simple Interest and Compound Interest formulas, definition with examples.
Interest formulas mainly refer to the formulas of simple and compound interests.
NoteWhen interest is calculated on the principal, or original amount. Then, it is known as Simple Interest.
NoteWhen interest is calculated on the principal amount and also on the interest of previous time periods. Then, it is known as Compound Interest .Compound Interest also known as Interest on interest.
Definition of Simple Interest
The interest calculated on the amount initially invested or loaned. It is a method for calculating the interest earned or paid on a certain balance in a specific period.
Simple interest is a quick and easy method of calculating the interest on a sum of Amount. It is determined by multiplying the daily interest rate by the principal amount and the number of days .
Definition Of Compound Interest
Compound interest is the addition of interest to the principal sum of a loan or deposit. Compound interest is calculated based on the principal, interest rate, and the time period involved.
It is the addition of interest to the sum of Amount or Principal Amount i.e. interest on interest. It is the result of reinvesting interest.So that interest in the next period is then earned on the principal amount and previously accumulated interest.
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Rate of interest (R)(in %) = n[(\frac{A}{P})^{\frac{1}{nT}} – 1]
Interest Compounded Half-Yearly
When interest is compounded Half yearly Then, we must consider n=2, Hence, Formula for Amount = \mathbf{P\left ( 1+\frac{R}{100\times 2} \right )^{2T}}
Compound Interest = Total amount – Principal
Rate of interest (R) (in %)= 2(P^{\frac{1}{2T}} – 1)
Interest Compounded Quarterly
We have to consider n=4. So, Amount = \mathbf{P\left ( 1+\frac{R}{100\times 4} \right )^{4T}}
Compound Interest = Total amount – Principal
Rate of interest (R) (in %)= 4(P^{\frac{1}{4T}} – 1)
Interest is Compound Monthly
When the interest is compounded montly then, n=12. So, formula for Amount = \mathbf{P\left ( 1+\frac{R}{100\times 12} \right )^{12T}}
Interest is Compounded Annually but Time is in Fraction, say 2(3/2) years
When the Interest is Compounded Annually but Time is in Fraction. Then, the formula Amount = P (1+r/100)2 * (1+(3/2)r/100)\mathbf{(1+ \frac{r}{100})^{2}}\mathbf{(1+ \frac{\frac{3r}{2}}{100})}
CI when Rates are Different for Different Years
When rates are different for different years . Then, Amount = P (1+ \frac{r_{1}}{100})(1+ \frac{r_{2}}{100})(1+ \frac{r_{3}}{100})
Formula for Simple Interest
Simple Interest
SI=\mathbf{\frac{P * R * T}{100}}
Where,
P = money borrowed or lent out for a certain period
r = rate of interest
t = time period for which the amount is lent
Principal = \frac{100 × SI}{R × T }
Rate = \frac{100 × SI}{P × T }
Time = \frac{100 × SI}{R × P }
Total Amount of Money
Amount = Principal + Interest
A = P + I
Question 1 : Vanraj shah borrowed a sum of Rs. 10,000 at 8% per annum compounded annually. If the amount is to be paid in three equal installments, the annual installment will be
Question 2 : A financier lends money at simple interest, but he includes the interest every six months for calculating the principal. If he is changing an interest of 20%, the effective rate of interest becomes?
Solution : Let the sum be Rs. 100. Then,
S.I. for first 6 months = \frac{100 * 20 * \frac{1}{2})}{100} = Rs.10
Next 6 months 20% of 110
S.I. for last 6 months =Rs.\frac{110 * 20 * \frac{1}{2})}{100} = Rs.11
So, amount at the end of 1 year = Rs. (100 + 10 + 11) = Rs. 121 R = (121 – 100) = 21%
Question 3 : Raghav singh purchases a coat for Rs.2400 cash or for Rs.1000 cash down payments and two monthly installments of Rs.800 each. Find the rate of interest.
Solution : Amount as a principal for 2 month = 2400 – 1000 = 1400 At the rate of r% per annum after 2 months,
Rs.1400 will amount to Rs 1400 + (\frac{1400*r*2}{100*12})
Total amount for 2 installments at the end of second month Rs800+(800+(\frac{800*r*1}{100*12)}))
Then 1400 + \frac{2800*r}{1200}=1600+ \frac{800*r}{1200} R=120%
Question 4: Mohsin khan invested Rs. 20,000 in a scheme at simple interest @ 15% per annum. After three years he withdrew the principal amount plus interest and invested the entire amount in another scheme for two years, which earned him compound interest @ 12% per annum. What would be the total interest earned by Mosses at the end of 5 years?
Question 5 : Bobby deol invested his money for a certain time. It amounts to Rs. 600 at 10% per annum. But when invested at 5% per annum, it amounts to Rs. 400. Find the time.
I can not see simple and compound interest quiz . could you provide me !
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