1. Calculate the amount and compound interest on 18,000 for 1(½) years at 10% per
annum compounded half yearly.​

2 thoughts on “1. Calculate the amount and compound interest on 18,000 for 1(½) years at 10% per<br />annum compounded half yearly.​”

1. Given :-

   • Principal = ₹18000
   • Time = 1½ years → 3/2 years
   • Rate = 10%
   • Compounded half-yearly

   Aim :-

   • To find the amount and compound interest

   Formula to use :-

   [tex] \longrightarrow \sf{amount = principal \bigg(1 + \dfrac{rate}{200} \bigg) ^{2 \times time}} [/tex]

   [tex] \longrightarrow \sf{compound \: interest = (amount) – (principal)}[/tex]

   Substituting the values,

   Amount :-

   [tex] \implies \sf{amount = 18000 \bigg( 1 + \dfrac{10}{200} \bigg)^{2 \times \frac{3}{2} } }[/tex]

   [tex] \implies \sf{amount = 18000 \bigg(1 + \dfrac{1 \not0}{20 \not0} \bigg)^{ \not2 \times \frac{3}{ \not2} } }[/tex]

   [tex] \implies \sf{amount = 18000 \bigg( \dfrac{20 + 1}{20} \bigg)^{3} }[/tex]

   [tex] \implies \sf{amount = 18000 \bigg( \dfrac{21}{20} \bigg)^{3} }[/tex]

   [tex] \implies \sf{amount = 18000 \times \dfrac{21}{20} \times \dfrac{21}{20} \times \dfrac{21}{20} }[/tex]

   [tex] \implies \sf{amount = 18 \not0 \not0 \not0 \times \dfrac{21}{2 \not0} \times \dfrac{21}{2 \not0} \times \dfrac{21}{2 \not0} }[/tex]

   Cancelling 18 and 2, as they are divisible,

   [tex] \implies \sf{amount = 9 \times 21 \times \dfrac{21}{2} \times \dfrac{21}{2} }[/tex]

   [tex] \implies \sf{ amount = \dfrac{83349}{4}}[/tex]

   [tex] \implies \sf{amount = 20837.25}[/tex]

   Amount = ₹20837.25

   Compound interest :-

   Substituting the values,

   [tex] \implies \sf{20837.25 – 18000}[/tex]

   [tex] \implies \sf{2837.25}[/tex]

   Compound interest = ₹2837.25

   Some more formulas :-

   • When interest is compounded yearly :-

   [tex] \longrightarrow \sf{amount = principal \bigg(1 + \dfrac{rate}{100} \bigg) ^{time} }[/tex]

   • When interest is compounded quarterly :-

   [tex] \longrightarrow \sf{amount = principal \bigg(1 + \dfrac{rate}{400} \bigg)^{4 \times time} }[/tex]

   • Simple interest :-

   [tex] \longrightarrow \sf{simple \: interest = \dfrac{principal \times rate \times time}{100} }[/tex]

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2. Answer:

   Principal = 18000

   Time = 3/2 years

   Rate = 10℅

   A = P(1+r/200)²*³/²

   = 18000(210/200)³

   = 18000*(9261/8000)

   = (166698/8000)

   Amount = 20837.25

   COMPOUND INTEREST = AMOUNT-PRINCIPAL

   = (20837.25-18000)

   = 2837.25

   HOPE IT HELPS YOU BRO.

   Reply