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Compound Interest Formula
P = principal amount (the initial amount you borrow or deposit)
r = annual rate of interest (as a decimal)
t = number of years the amount is deposited or borrowed for.
A = amount of money accumulated after n years, including interest.
n = number of times the interest is compounded per year
Example:
An amount of $1,500.00 is deposited in a bank paying an annual interest rate of 4.3%, compounded quarterly. What is the balance after 6 years?
Solution:
Using the compound interest formula, we have thatP = 1500, r = 4.3/100 = 0.043, n = 4, t = 6. Therefore,
So, the balance after 6 years is approximately $1,938.84.
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How can compound interest be derived from simple interest?
Compound interest is simply simple interest except the amount of interest you owe is always added into the amount of money you borrowed before you calculate.Lets give an example.You borrowed a million from the bank at Year 2000 with interest rates of 5%.The formula for simple interest is PIN/100, where P is Principle (amount owed), I is interest rate (in percentage), N is the number of years.Year 2000: 1,000,000Year 2001: 1,000,000 * 5 * 1 / 100 = 50,000 (this is the interest)Year 2002: (1,000,000 + 50,000) * 5 * 1 / 100 = 52,500By the end of 2002, you would owe the bank 1,102,500(1,000,000 + 50,000 + 52,500)The formula for compound interest is P * (1 + I/100)N where P,I and N still refers to the same thing.Year 2000: 1,000,000Year 2001: 1,000,000 * (1+5/100)1 = 1,050,000Year 2002: 1,050,000 * (1+5/100)1 = 1,000,000 * (1+5/100)2 = 1,102,500
The concepts of simple interest and compound interest?
With simple interest, you just multiply the capital, the number of years, and the yearly interest rate. For example, for a capital of 10,000 dollars, 3% interest, 10 years, that would give you 10,000 x 3/100 x 10 = 3,000 dollars interest.With compound interest, after the end of every year, the interest is added to the capital, before calculating the interest for next year.In the example above, the first year you get 10,000 x 0.03 = 300 dollars. This is then added to the capital, before calculating the interest rate for the next year; so, the second year you get 10,300 x 0.03 = 309 dollars interest.
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How can compound interest be derived from simple interest?
Compound interest is simply simple interest except the amount of interest you owe is always added into the amount of money you borrowed before you calculate.Lets give an example.You borrowed a million from the bank at Year 2000 with interest rates of 5%.The formula for simple interest is PIN/100, where P is Principle (amount owed), I is interest rate (in percentage), N is the number of years.Year 2000: 1,000,000Year 2001: 1,000,000 * 5 * 1 / 100 = 50,000 (this is the interest)Year 2002: (1,000,000 + 50,000) * 5 * 1 / 100 = 52,500By the end of 2002, you would owe the bank 1,102,500(1,000,000 + 50,000 + 52,500)The formula for compound interest is P * (1 + I/100)N where P,I and N still refers to the same thing.Year 2000: 1,000,000Year 2001: 1,000,000 * (1+5/100)1 = 1,050,000Year 2002: 1,050,000 * (1+5/100)1 = 1,000,000 * (1+5/100)2 = 1,102,500
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