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
Let's understand the workings of the simple interest calculator 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.
What will be the compound interest on $25,000 after 3 years at 12% per annum? ›
25000 after 3 years at the rate of 12 per cent p.a.? Rs. 10123.20.
How much interest will you earn from the $1000 bond that pays 5% interest annually and matures in 5 years? ›
You obtain a $1,000 bond that pays 5% interest annually that matures in 5 years. How much interest will you earn? Each year, you would earn 5% interest: $1000(0.05) = $50 in interest. So over the course of five years, you would earn a total of $250 in interest.
How much is $1000 worth at the end of 2 years if the interest rate of 6% is compounded daily? ›
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 formula for compound interest and examples? ›
The compound interest is found using the formula: CI = P( 1 + r/n)nt - P. In this formula, P( 1 + r/n)nt represents the compounded amount. the initial investment P should be subtracted from the compounded amount to get the compound interest.
What is the simple interest formula example? ›
For calculating simple interest, Simple Interest = (P x T x R)/ 100 = (5000 x 2 x 5)/ 100 = 500 Rs. So, Shravan will have a total of 5500 Rs. at the end of two years.
How much will the coupon payments be of a 30 year $10000 bond with a 4.5% coupon rate and semi annual payments? ›
Answer and Explanation:
The value of coupon payments will be $225.
How much is $10000 for 5 years at 6 interest? ›
Summary: An investment of $10000 today invested at 6% for five years at simple interest will be $13,000.
What is $5000 invested for 10 years at 10 percent compounded annually? ›
The future value of the investment is $12,968.71. It is the accumulated value of investing $5,000 for 10 years at a rate of 10% compound interest.
What is the future value of $1000 after 5 years at 8% per year? ›
Answer and Explanation: The future value of a $1000 investment today at 8 percent annual interest compounded semiannually for 5 years is $1,480.24.
Given this, you plug a principal amount of $1,000,000, a rate of 3.18% and a time of 30 years into the compound interest formula. And voila, in 30 years the equivalent of $1,000,000 would be $2,557,794 and some change.
How much is $100 received at the end of each year forever at 10% interest worth today? ›
So, a $100 at the end of each year forever is worth $1,000 in today's terms.
How is compound and simple interest calculated? ›
Simple interest is calculated by multiplying the loan principal by the interest rate and then by the term of a loan. Compound interest multiplies savings or debt at an accelerated rate. Compound interest is interest calculated on both the initial principal and all of the previously accumulated interest.
What is the easiest way to calculate compound interest? ›
How Compound Interest Works. Compound interest is calculated by multiplying the initial principal amount by one plus the annual interest rate raised to the number of compound periods minus one. The total initial principal or amount of the loan is then subtracted from the resulting value.
What is the easiest way to calculate simple interest? ›
The formula to determine simple interest is an easy one. Just multiply the loan's principal amount by the annual interest rate by the term of the loan in years. This type of interest usually applies to automobile loans or short-term loans, although some mortgages use this calculation method.
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.
