The simple interest on a certain sum of money for 3 years at 5% p.a is Rs 1200. Find theamount due and the compound interest on this sum of money at the same rate after 3years, interest is reckoned annually.
Question
The simple interest on a certain sum of money for 3 years at 5% p.a is Rs 1200. Find theamount due and the compound interest on this sum of money at the same rate after 3years, interest is reckoned annually.
Solution
First, let's find the principal amount using the simple interest formula:
Simple Interest = (Principal * Rate * Time) / 100
Given that Simple Interest = Rs 1200, Rate = 5% per annum, and Time = 3 years, we can substitute these values into the formula and solve for the Principal:
1200 = (Principal * 5 * 3) / 100 1200 = (Principal * 15) / 100 Principal = (1200 * 100) / 15 Principal = Rs 8000
Now, let's find the amount due and the compound interest using the compound interest formula:
Amount = Principal * (1 + Rate/100) ^ Time
Substituting the values we have:
Amount = 8000 * (1 + 5/100) ^ 3 Amount = 8000 * (1.05) ^ 3 Amount = Rs 9261
The compound interest is then the Amount minus the Principal:
Compound Interest = Amount - Principal Compound Interest = 9261 - 8000 Compound Interest = Rs 1261
So, the amount due is Rs 9261 and the compound interest is Rs 1261.
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