COMPOUND INTEREST –
If the interest, due on a certain sum of money (Principal) after a particular period of time (Usually 1 year ) is not paid to the lender, but added to the principal, i.e., compounded with the principal then the sum of money is said to be lent at compound interest. In other words, when money is lent or invested at compound interest, the principal increases each year (or other periods) by the addition of interest. So, the annual interest also increases.
The total sum owed after any given period is called the amount at compound interest for that period, and the compound interest is the difference between the amount and the original principal.
Compound Interest (CI) = amount – original principal.
Banks, insurance, and other financial companies or hubs calculate interest in this way.
Example.
1) Find the compound interest on $ 2000 for 3 years at the rate of 15% per annum. Also, find the amount at the end of the period.
Answer) Here, Principal (P) = $ 2000, Rate (R) = 15%
So, as per the rules, the interest for the first year =
P X R X T 2000 X 15 X 1
-------------- = ---------------- = $ 300
100 100
The amount after the first year = $ 2000 + $ 300 = $ 2300
So, the principal for the second year = $ 2300
Now, the interest on the second year =
P X R X T 2300 X 15 X 1
--------------- = ----------------- = $ 345
100 100
The amount after the second year = $ 2300 + $ 345 = $ 2645
So, the principal for the third year = $ 2645
Now, the interest on the second year =
P X R X T 2645 X 15 X 1
-------------- = ----------------- = $ 396.75
100 100
The amount after the third year = $ 2645 + $ 396.75 = $ 3041.75
So, the final principal at the end of the third year = $ 3041.75
So, the compound interest is = $ 3041.75 - $ 2000 = $ 1041.75 (Ans.)
2) Calculate the compound interest on $ 24,000 for 5 years at 10% per annum.
Answer) Here, Principal (P) = $ 24000, Rate (R) = 10%
So, as per the rules, the interest for the first year =
P X R X T 24000 X 10 X 1
-------------- = ------------------ = $ 2400
100 100
The amount after the first year = $ 24000 + $ 2400 = $ 26400
So, the principal for the second year = $ 26400
Now, the interest on the second year =
P X R X T 26400 X 10 X 1
--------------- = ------------------- = $ 2640
100 100
The amount after the second year = $ 26400 + $ 2640 = $ 29040
So, the principal for the third year = $ 29040
Now, the interest on the third year =
P X R X T 29040 X 10 X 1
--------------- = ------------------- = $ 2904
100 100
The amount after the third year = $ 29040 + $ 2904 = $ 31944
So, the principal of the fourth year = $ 31944
Now, the interest on the fourth year =
P X R X T 31944 X 10 X 1
------------ = ------------------- = $ 3194.4
100 100
The amount after the fourth year = $ 31944 + $ 3194.4 = $ 35138.4
So, the principal for the fifth year = $ 35138.4
Now, the interest on the fifth year =
P X R X T 35138.4 X 10 X 1
--------------- = -------------------- = $ 3513.84
100 100
The amount after the fourth year = $ 35138.4 + $ 3513.84 = $ 38652.24
So, the principal at the end of fifth year = $ 38652.24
So, the compound interest is = $ 38652.24 - $ 24000
= $ 14652.24 (Ans.)
3) Find the compound interest on $ 22000 for 2 years, the rate of interest being 5% per annum for the first year and 10% per annum for the second year. Also, find the amount at the end of the period.
Answer) Here, Principal (P) = $ 22000, Rate (R) = 5%
So, as per the rules, the interest for the first year =
P X R X T 22000 X 5 X 1
-------------- = ------------------ = $ 1100
100 100
The amount after the first year = $ 22000 + $ 1100 = $ 23100
So, the principal for the second year = $ 23100
Now, the interest on the second year =
P X R X T 23100 X 10 X 1
--------------- = ------------------ = $ 2310
100 100
The amount after the second year = $ 23100 + $ 2310
= $ 25410…………………….. (2)
So, the compound interest is = $ 25410 - $ 22000
= $ 3410………………….……. (1) (Ans.)