Compound interest. Examples of the calculation of compound interest.
A formula for calculating annual compound interest
|P = A(1 +||I||)n|
A - is the original principal;
I - nominal annual interest rate in percentage terms;
n - number of compounding periods.
The derivation of formula for calculating compound interest
- To calculate the value for one period we use the formula to calculate the number that is greater than the original number of a given percentage
P1 = A(1 + I ) 100%
- for the second period
P2 = P1(1 + I ) = A(1 + I )2 100% 100% . . .
- for the n-th period
Pn = Pn-1(1 + I ) = A(1 + I )n 100% 100%
Examples of problems with compound interest
Solution. Use the formula for calculating compound interest:
|P = 30,000(1 +||10%||)3 = 30,000 · 1.13 = 39,930|
Answer: profit is $ 9,930.
If you put in the bank A dollars, then after a year we get:
|P = A(1 +||12%||)|
If the interest accrued each month with an interest rate of x, then after a year (12 months)
|P = A(1 +||x||)12|
Equating these values we obtain the equation, the solution of which will determine the monthly interest rate
|A(1 +||12%||) = A(1 +||x||)12|
|1.12 = (1 +||x||)12|
Answer: monthly interest rate is equal 0.9488792934583046%.
N.B. From this task you can see that the monthly interest rate is not equal to the annual interest rate divided by 12.
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