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A sum of Rs.100 is lent at simple interest of 3% p.a for the first month 9% p.a. for the second month, 27% p.a. for the third month and so on .what is the total amount of interest earned at the end of one year approximately ?
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A sum of Rs.100 is lent at simple interest of 3% p.a for the first mon...
Calculation of Total Interest Earned
Given:
- Principal amount = Rs.100
- Interest rate for the first month = 3% p.a.
- Interest rate for the second month = 9% p.a.
- Interest rate for the third month = 27% p.a.
- Interest rate for the subsequent months = Three times the previous month's interest rate.
To Find:
- Total interest earned at the end of one year approximately.
Calculation:
Let us find the interest earned for each month separately and then add them up.
Month 1:
Simple interest for the first month = (100 x 3 x 1)/100 = Rs.3
Month 2:
Simple interest for the second month = (100 x 9 x 1)/100 = Rs.9
Month 3:
Simple interest for the third month = (100 x 27 x 1)/100 = Rs.27
Month 4:
Simple interest for the fourth month = (100 x 81 x 1)/100 = Rs.81
Month 5:
Simple interest for the fifth month = (100 x 243 x 1)/100 = Rs.243
Month 6:
Simple interest for the sixth month = (100 x 729 x 1)/100 = Rs.729
Month 7:
Simple interest for the seventh month = (100 x 2187 x 1)/100 = Rs.2187
Month 8:
Simple interest for the eighth month = (100 x 6561 x 1)/100 = Rs.6561
Month 9:
Simple interest for the ninth month = (100 x 19683 x 1)/100 = Rs.19683
Month 10:
Simple interest for the tenth month = (100 x 59049 x 1)/100 = Rs.59049
Month 11:
Simple interest for the eleventh month = (100 x 177147 x 1)/100 = Rs.177147
Month 12:
Simple interest for the twelfth month = (100 x 531441 x 1)/100 = Rs.531441
Total interest earned at the end of one year = Rs.720720
Final Answer:
The total amount of interest earned at the end of one year approximately is Rs.720720.
Community Answer
A sum of Rs.100 is lent at simple interest of 3% p.a for the first mon...
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A sum of Rs.100 is lent at simple interest of 3% p.a for the first month 9% p.a. for the second month, 27% p.a. for the third month and so on .what is the total amount of interest earned at the end of one year approximately ?
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