Question

find the compund interest on 1000 at the rate of 10% per annum from 18 months when intereste in compound in half year?​

Answer 1

Given:

• Principal = 1000
• Rate = 10%
• Time = 18 months

To find:

• The compound interest?

Solution:

By using formula,

• A = P ( 1 + R/200)^2n

Where,

• P = 1000
• R = 10%
• 2n = 3 years.

• Let the compound interest be C.I.

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« Now, By using the formula,

• A = P ( 1 + R/200)^2n

Now, Putting values,

→ A = 1000(1 + 10/200)^3

→ A = 1000(210/200)^3

→ A = 1000(1.05)^3

→ A = 1000(1.157)

→ A = 1157.625

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« Now, Let's find C.I,

As we know that,

→ C.I = A - P

→ 1157.625 - 1000

→ 157.625

∴ Hence, Compound interest on 1000 at the rate of 10% is 157.625.

Answer 2

⠀⠀⠀⠀⠀⠀${\rm{\purple{\underline{\underline{★Required \:Answer★}}}}}$

157.625

⠀⠀⠀⠀⠀${\rm{\pink{\underline{\underline{★Solution★}}}}}$

${\rm{\red{\underline{\underline{Given : }}}}}$

Principal (P) = 1000

Rate (r) = 10% per annum

Number of times interest applied per time period (n) = 18 months = $\rm\frac{18}{12} \: years = \frac{3}{2} \: years = 1 \frac{1}{2} \: years$

Amount (A) = ?

${\rm{\blue{\underline{\underline{To \: Find: }}}}}$

• Compound interest

${\rm{\purple{\underline{\underline{Formula \: Used: }}}}}$

$\rm \: C.I. = A - P$

$\rm A = P(1 + \frac{r}{n} ) {}^{2n}$

where,

C.I = Compound interest

A = final amount

P = Principal

r = interest rate

n = number of times interest applied per time period

${\rm{\orange{\underline{\underline{Calculations : }}}}}$

Amount after 18 years =

$\rm \: P[1 + \frac{1}{2} ( \frac{r}{100} )] {}^{2n}$

$\longmapsto \rm \: 1000[1 + \frac{1}{2} ( \frac{10}{100} )] {}^{2 \times \frac{3}{2} }$

$\longmapsto \rm \: 1000[1 + \frac{10}{200} ] {}^{3}$

$\longmapsto 1000( \frac{200 + 10}{200} ) {}^{3}$

$\longmapsto1000( \frac{ \cancel{210}} { \cancel{200}}) {}^{3}$

$\longmapsto1000( \frac{21}{20} ) {}^{3}$

$\longmapsto1000 \times \frac{21}{20}\times \frac{21}{20} \times \frac{21}{20}$

$\longmapsto1157.625$

As we know,

$\rm \: C.I = A - P$

substituting the values,

$\longmapsto \rm \: C.I \: = 1157.625 - 1000$

$\longmapsto \rm \: C.I = 157 .625$