Question

Calculate how many years it will take to earn the given amount of interest in each of the following cases:
a)principle $2000 rate 10% interest $500

b)principle $75000 rate4% interest$1500

Answer 1

Answer:

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Answer 2

${\huge{\boxed{\mathrm{\underline{\green{A}{\red{n}{\blue{s}{\orange{w}{\purple{e}{\pink{r}{\green{:-}}}}}}}}}}}}$

a) 2.5 years (2 years 6 months)

b) 0.5 years (6 months)

Step-by-step explanation:

${\mathrm{\underline{\red{In \ first \ question:-}}}}$

${\large{\mathrm{\green{\underline{Given:-}}}}}$

• Principal = $2,000
• Rate = 10%
• Interest = $500

${\large{\mathrm{\orange{\underline{To \ Find:-}}}}}$

• Time

${\large{\mathrm{\pink{\underline{Formula \ Used:-}}}}}$

${\mathsf{\orange{Simple \ Interest = \dfrac{Principal \times Rate \times Time}{100}}}}$

After Transposing,

${\blue{\mathsf{Time = \dfrac{Simple \ Interest \times 100}{Principal \times Rate}}}}$

${\large{\mathrm{\blue{\underline{Solution:-}}}}}$

After inserting the values in the formula of time,

${\green{\mathsf{Time = \dfrac{\ 500 \times 100}{\ 2000 \times 10} \ years}}}$

$\Longrightarrow {\mathsf{\dfrac{5 \times 1}{2 \times 1} \ years}}$

$\Longrightarrow {\mathsf{\dfrac{5}{2} \ years}}$

$\Longrightarrow {\mathsf{2.5 \ years}}$

${\boxed{\mathsf{\pink{\therefore \ Time = 2.5 \ years}}}}$

${\mathrm{\underline{\red{In \ second \ question:-}}}}$

${\large{\mathrm{\green{\underline{Given:-}}}}}$

• Principal = $75,000
• Rate % = 4%
• Interest = $1,500

${\large{\mathrm{\orange{\underline{To \ Find:-}}}}}$

• Time

${\large{\mathrm{\pink{\underline{Formula \ Used:-}}}}}$

${\mathsf{\orange{Simple \ Interest = \dfrac{Principal \times Rate \times Time}{100}}}}$

After Transposing,

${\green{\mathsf{Time = \dfrac{Simple \ Interest \times 100}{Principal \times Rate}}}}$

${\large{\mathrm{\blue{\underline{Solution:-}}}}}$

After inserting the values in the formula of time,

${\pink{\mathsf{Time = \dfrac{\ 1500 \times 100}{\ 75000 \times 4} \ years}}}$

$\Longrightarrow {\mathsf{\dfrac{15 \times 25}{750 \times 1} \ years}}$

$\Longrightarrow {\mathsf{\dfrac{375}{750} \ years}}$

$\Longrightarrow {\mathsf{\dfrac{1}{2} \ years = 0.5 \ years}}$

${\boxed{\mathsf{\blue{\therefore \ Time = 0.5 \ years}}}}$