Question

Find the time (in years) in which Rs12500 will produce Rs3246.40 as compound interest at
8% per annum, compounded annually.
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Answer 1

Given :-

• Principal (P) = Rs.12500
• Compound interest (C.I) = Rs.3246.40
• Rate of interest (R) = 8%

To find :-

• Time (in years) = ?

Solution :-

Compound Interest = Amount - Principal

→Amount = C.I + P

→ A = 3246.40 + 12500

→ A = Rs.15746.4

Now,

→ Amount = P(1 + R/100)ⁿ

→ 15746.4 = 12500(1 + 8/100)ⁿ

→ 15746.4/12500 = (1 + 2/25)ⁿ

→ 157464/12500 × 10 = (25 + 2/25)ⁿ

→ 39366/31250 = (27/25)ⁿ

→ 19683/15625 = (27/25)ⁿ

→ 27 × 27 × 27/25 × 25 × 25 = (27/25)ⁿ

→ (27/25)³ = (27/25)ⁿ

→ n = 3

•°• Time = 3 years

More to know

• Simple Interest = P × R × T/100

• Amount = Principal + S.I

________________________________

Answer 2

$\huge{\boxed{\bold{Question}}}$

Find the time (in years) in which Rs12500

will produce Rs3246.40 as compound

interest at

8% per annum, compounded annually.

$\huge{\boxed{\bold{Given}}}$

Principal ,p=Rs12500

Rate of interest ,r=8%

Interest =Rs 3246.40

To find,

Number of year.

Solution

We applly component interest formula

${\boxed { \boxed{ \boxed { \bold{ \rm \: component \: interest \: p = (1 + \frac{r}{ 100}) ^{n} - p }}}}}\\ \implies \rm \: 3246.40 = 12500(1 + \frac{8}{100} ) ^{n} - 12500 \\ \\ \\ \implies \rm \: 3246.40 + 12500 = 12500(1 + \frac{2}{25} ) ^{n} \\ \\ \\ \implies \rm \: 15746.40 = 12500(1 + \frac{2}{25} ) ^{n} \\ \\ \\ \implies \rm \: \frac{15746.40}{12500} = ( \frac{27}{25} ) ^{n} \\ \\ \\ \implies \rm \: \frac{157464}{125000} = ( \frac{27}{25} ) ^{n} \\ \\ \\ \implies \rm \: \frac{78732}{62500} = ( \frac{27}{25} ) ^{n} \\ \\ \\ \implies \rm \: \frac{39366}{31250} = ( \frac{27}{25} ) {}^{n} \\ \\ \\ \implies \rm \: \frac{19683}{15625} = ( \frac{27}{25} ) ^{n} \\ \\ \\ \implies\tt \: \frac{27 \times 27 \times 27}{25 \times 25 \times 25} = ( \frac{27}{25}) ^{n} \\ \\ \\ \\ \tt \: equating \: \: power \: \: on \: \: both \: \: sides \: \: \\ \\ \boxed{ \rm \: we \: get} \\ \\ \blue{ \tt \: n = 3} \\ \\ \boxed{ \sf \: 3years \: \: answer}$

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