Simple and Compound Interests
1. Simple Interest (SI) formula
SI=P×R×T100
where,
P – Principal or the original sum borrowed
R – Rate of interest. It is the rate at which the interest is calculated on the original sum
T – Time for which the original sum is borrowed. It is also denoted as ‘n’
2. Amount (A) = Principal + Simple Interest
A=P×1+R×T100
3. Compound Interest Formula
Amount after 'n' years =P×1+R100n
4. Given the amount and principal, the interest is
I=A-P=P×1 +R100n-1
5. Amount in Compound interest case is given by
A=P×1+R100T
6. When rates are different for different years, say r1, r2, r3 percent for 1st, 2nd and 3rd year respectively, the amount can be calculated as
A=P(1+r1)100(1+r2)100(1+r3 )1007.
| Simple Interest and Compound Interest Differences | ||
Parameter | Simple Interest | Compound Interest |
| Definition | Simple Interest can be defined as the sum paid back for using the borrowed money, over a fixed period of time. | Compound Interest can be defined as when the sum principal amount exceeds the due date for payment along with the rate of interest, for a period of time. |
| Formula | S.I.=(P × T × R)100 | C.I.=P1+R100t−P |
| Return Amount | The return is much lesser when compared to Compound Interest. | The return is much higher. |
| Principal Amount | The principal amount is constant | The principal amount keeps on varying during the entire borrowing period |
| Growth | The growth remains quite uniform in this method. | The growth increases quite rapidly in this method. |
| Interest Charged | The interest charged on is for the principal amount. | The interest charged on it is for the principal and accumulated interest. |
Q.
By using the formula, find the amount and compound interest on:
Rs.62500 for 2 years 6 months at 12% per annum compounded annually.
Q.
By using the formula, find the amount and compound interest on:
A machine is purchased for Rs 625000. Its value depreciates at the rate of 8% per annum. What will be its value after 2 years ?
Q.
By using the formula, find the amount and compound interest on:
A scooter is bout at Rs 56000. Its value depreciates at the rate of 10% per annum. What will be its value after 3 years ?
Q.
By using the formula, find the amount and compound interest on:
The difference between the compound interest and the simple interest on a certain sum for 2 years at 6% per annum is Rs 90. Find the sum.
Q.
By using the formula, find the amount and compound interest on:
A sum of money amounts to Rs 10240 in 2 years at 623% per annum, compounded annually. Find the sum.
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The difference between the compound interest and the simple interest on a sum at 10% p.a. for three years is Rs. 155. The sum (in Rs.) is:
- 5,500
- 6,600
- 5,000
- 6,000
Answer (Detailed Solution Below)
Option 3 : 5,000
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Compound interest = x(1 + r/100)n – x
Simple interest = x × r × t/100
According to question,
x(1 + 10/100)3 – x – x × 10 × 3/100 = 155
⇒ x(1331/1000 – 1 – 3/10) = 155
⇒ x = 155000/31 = 5000
∴ The sum is Rs. 5000
Last updated on Sep 22, 2022
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