Interest formulas mainly refer to the formulas of simple and compound interests. The simple interest (SI) is a type of interest that is applied to the amount borrowed or invested for the entire duration of the loan, without taking any other factors into account, such as past interest (paid or charged) or any other financial considerations. Simple interest is generally applied to short-term loans, usually one year or less, that are administered by financial companies. The same applies to money invested for a similarly short period of time. The simple interest rate is a ratio and is typically expressed as a percentage.
On the other hand, the compound interest is the interest which is calculated on the principal and the interest that is accumulated over the previous tenure. Thus, the compound interest (CI) is also called “interest on interest”. It plays an important role in determining the amount of interest on a loan or investment. The formulas for both the compound and simple interest are given below.
Interest Formulas for SI and CI
The Interest formulas are given as,
| Formulas for Interests (Simple and Compound) |
|---|
| SI Formula | S.I. = Principal × Rate × Time |
| CI Formula | C.I. = Principal (1 + Rate)Time − Principal |
Example Problems Using Interest Formulas
Question 1:A sum of Rs 4000 is borrowed and the rate is 7%. What is the simple and compound interest for 2 years?
Solution:
Simple Interest = Principle × Rate × Time = PTR/100
⇒ Simple Interest = 4000 × (7 ⁄ 100) × 2
⇒ Simple Interest = 560
∴ The simple Interest for 2 years is Rs. 560
Compound Interest = Principal × (1 + Rate)Time − Principal
So, Compound Interest = 4000 × (1 + 7 ⁄ 100)2 − 4000
⇒ Compound Interest = (4000 × 1.1449) − 4000
⇒ Compound Interest = 580
∴ The compound interest for 2 years is Rs. 580
Question 2: A sum of Rs. 25000 becomes Rs. 30000 at the end of 4 years when calculated at simple interest. Find the rate of interest.
Solution:
Given,
Principal = P = Rs. 25000
Time = T = 4 years
Amount at the end of 4 years = Rs. 30000
SI = Rs. 30000 – Rs. 25000 = Rs. 5000
SI = PTR / 100
⇒ R = SI × 100 / PT
⇒ R = 5000 × 100 /( 25000× 4)
⇒ R = 5%
Hence, the rate of interest = 5%
Question 3: Find the compound interest on Rs. 13000 at 10% for 2 years, compounded annually.
Solution:
Given,
Principal = P = Rs. 13000
Rate of interest = r = 10%
Time = t = 2 years
Amount on CI = P(1 + r/100)2
= 13000(1 + 10/100)2
= 13000 (1 + 0.1)2
= 13000(1.1)2
= 13000 × 1.21
= 15730
CI = Amount on CI – Principal
= Rs. 15730 – Rs. 13000
= Rs. 2730
Therefore, the compound interest = Rs. 2730
More Interest Related Formulas
FAQs
Interest Formulas for SI and CI
| Formulas for Interests (Simple and Compound) |
|---|
| SI Formula | S.I. = Principal × Rate × Time |
| CI Formula | C.I. = Principal (1 + Rate)Time − Principal |
What Is the Monthly Compound Interest Formula? The monthly compound interest formula is given as CI = P(1 + (r/12) )12t - P. Here, P is the principal (initial amount), r is the interest rate (for example if the rate is 12% then r = 12/100=0.12), n = 12 (as there are 12 months in a year), and t is the time.
What is the simple interest earned on a 1 year investment of $500 at a 6% annual interest rate? ›
In one year the interest he will earn is I = (500)(0.06)(1) = $30.
What is the compound interest on a three year $100.00 loan at a 10 percent annual interest rate? ›
Summary: The compound interest on a three-year, $100.00 loan at a 10 percent annual interest rate is $ 33.1.
What is the easiest way to calculate simple interest? ›
The simple interest formula allows us to calculate I, which is the interest earned or charged on a loan. According to this formula, the amount of interest is given by I = Prt, where P is the principal, r is the annual interest rate in decimal form, and t is the loan period expressed in years.
Are there 2 formulas for compound interest? ›
The formula we use to find compound interest is A = P(1 + r/n)^nt. In this formula, A stands for the total amount that accumulates. P is the original principal; that's the money we start with. The r is the interest rate.
How much is $1000 worth at the end of 2 years if the interest rate of 6% is compounded daily? ›
Basic compound interest
For other compounding frequencies (such as monthly, weekly, or daily), prospective depositors should refer to the formula below. Hence, if a two-year savings account containing $1,000 pays a 6% interest rate compounded daily, it will grow to $1,127.49 at the end of two years.
What is the easiest way to calculate compound interest? ›
The formula for calculating compound interest is: Compound interest = total amount of principal and interest in future (or future value) minus principal amount at present (or present value)
What is the formula for simple interest? ›
The formula for simple interest is SI = P × R × T / 100, where SI = simple interest, P = principal amount, R = the interest rate per annum, and T = the time in years.
How do you convert simple interest to compound interest? ›
You can calculate compound interest with this Formula: (A = P (1 + R/N) ^ nt).
The simple interest formula is given by I = PRt where I = interest, P = principal, R = rate, and t = time. Here, I = 10,000 * 0.09 * 5 = $4,500. The total repayment amount is the interest plus the principal, so $4,500 + $10,000 = $14,500 total repayment.
What is the simple interest on 7500 at 8% per annum per 1 year 6 months? ›
Detailed Solution
- Given: Principal = Rs. 7,500. Rate of Interest = 8% per annum. ...
- Formula Used: SI = PRT/100. where, SI = Simple Interest, ...
- Calculation: According to the question, SI = PRT/100. ⇒ {7500 × 8 × (3/2)}/100. ...
- ∴ The simple interest on 7,500 at 8% per annum per 1 year 6 months is Rs. 900.
But we need to multiply 85 by 6 year which give us: 510. We now add 1,000 and 510 together which gives us 1,510.
How long will it take $1000 to double at 6% simple interest? ›
So, if the interest rate is 6%, you would divide 72 by 6 to get 12. This means that the investment will take about 12 years to double with a 6% fixed annual interest rate.
What is the formula for the difference between simple interest and compound interest? ›
Simple Interest (SI): SI=P×R×T÷100, where P is the principal amount, R is the rate of interest, and T is the time in years. Compound Interest (CI): CI=P×(1+100R)T−P where P is the principal amount, R is the rate of interest, and T is the time in years.
What is the simple interest on Rs 4000 at an annual rate of interest of 5 for 6 months? ›
Expert-Verified Answer. The simple interest on Rs4000 at an annual rate of interest of 5% for 6 months is Rs 1. Therefore, The simple interest on Rs4000 at an annual rate of interest of 5% for 6 months is Rs 1.
How to calculate interest with an example? ›
The principal amount is Rs 10,000, the rate of interest is 10% and the number of years is six. You can calculate the simple interest as: A = 10,000 (1+0.1*6) = Rs 16,000. Interest = A – P = 16000 – 10000 = Rs 6,000.
