Finding the Time Period for Compound Interest
by Nirmal
(Dubai)
Question
in what time the compound interest on Rs800 at 20% per annum will amount to Rs1152 if compounded annually?
Answer
STEP 1The compound interest formula is given below:
![compound interest formula](data:image/png;base64,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)
Where:
- A is the total amount of money (including interest) after n years
- P is the principal (the amount money borrowed or invested)
- r is the interest rate (per year or per annum)
- n is the loan or investment duration in years
STEP 2Thus, let us substitute the values we have into the formula:
1152 = 800(1+0.2)^n
STEP 3We can then proceed to solve the equation:
1152/800 = (1.2)^n
1.44 = (1.2)^n
1.44 = (1.2)^2
Thus, it takes
two years for the compound interest to amount to Rs1152.
You can also refer to our tutorial on
how to calculate compound interest.