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Find the sum on which the compound interest for 3 years at
10% per annum amounts to ₹ 1,655 .

$7$ . Find the sum on which the compound interest for $3$ years at $10 \%$ per annum amounts to ₹ $1$ , $655$ .

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Finance problems

Full solution

Q.

7

. Find the sum on which the compound interest for

3

years at

10 \%

per annum amounts to ₹

1

,

655

.

Understand Compound Interest Formula: We know the formula for compound interest is $A = P(1 + \frac{r}{n})^{nt}$ , where $A$ is the amount after $t$ years, $P$ is the principal amount, $r$ is the annual interest rate, and $n$ is the number of times interest is compounded per year. Here, $A = P +$ compound interest, $r = 10\%$ or $0.10$ , $n = 1$ (since it's compounded annually), and $A$ $0$ years.
Write Equation with Given Values: Given that the compound interest is ₹ $1$ , $655$ , we can write the equation as $P(1 + \frac{0.10}{1})^{(1\times3)} - P = 1,655$ .
Simplify the Equation: Simplify the equation: $P(1 + 0.10)^3 - P = 1,655$ .
Calculate Exponential Value: Calculate $(1 + 0.10)^3$ : $(1.10)^3 = 1.10 \times 1.10 \times 1.10 = 1.331$ .
Substitute Value into Equation: Substitute the value back into the equation: $P \times 1.331 - P = 1,655$ .
Factor Out Principal Amount: Factor out $P$ : $P(1.331 - 1) = 1,655$ .
Calculate Difference: Calculate $1.331 - 1$ : $1.331 - 1 = 0.331$ .
Isolate Principal Amount: Now we have $P \times 0.331 = 1,655$ .
Calculate Principal Amount: Divide both sides by $0.331$ to find $P$ : $P = \frac{1,655}{0.331}$ .
Calculate Principal Amount: Divide both sides by $0.331$ to find $P$ : $P = \frac{1,655}{0.331}$ .Calculate $P$ : $P = 5000$ .

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