On a certain sum, rate of interest per annum for the first two years is 4%. The rate of interest for next four years is 6% and for the next three years is 8%. If total simple interest earned at the end of 9 years is ₹ 1120, then the sum is:
₹2000
The problem asks us to find the principal sum (P) given the total simple interest earned over 9 years with varying interest rates during different periods.
Calculating Total Simple Interest Components
The total simple interest (SI) is the sum of the simple interest earned in each phase.
- Phase 1: First 2 years at 4% per annum. SI$_1$ = $ \frac{P \times 4 \times 2}{100} = \frac{8P}{100} $
- Phase 2: Next 4 years at 6% per annum. SI$_2$ = $ \frac{P \times 6 \times 4}{100} = \frac{24P}{100} $
- Phase 3: Next 3 years at 8% per annum. SI$_3$ = $ \frac{P \times 8 \times 3}{100} = \frac{24P}{100} $
Formulating the Simple Interest Equation
The total simple interest earned is given as ₹ 1120.
Total SI = SI$_1$ + SI$_2$ + SI$_3$
$ 1120 = \frac{8P}{100} + \frac{24P}{100} + \frac{24P}{100} $
Solving for the Principal Sum (P)
Combine the terms on the right side:
$ 1120 = \frac{(8 + 24 + 24)P}{100} $
$ 1120 = \frac{56P}{100} $
Now, isolate P:
$ P = \frac{1120 \times 100}{56} $
Calculate the value:
$ P = \frac{112000}{56} $
$ P = 2000 $
Therefore, the principal sum is ₹ 2000.
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