calculate the amount on a sum of 1600 for 1 1/2 years at rate of 10% per annum compound interest when interest is added half yearly
Answers
Answer:
C. I. = 168.2 ans.
\Large{\underline{\underline{\bf{GiVen:-}}}}
GiVen:−
❥ P(principal) = ₹1,600
❥ R(rate) = 10%.
❥ N(time) = 1½ years.
\Large{\underline{\underline{\bf{To Find:-}}}}
ToFind:−
❥ The compound interest which is compounded half - yearly.
\Large{\underline{\underline{\bf{SoLuTion:-}}}}
SoLuTion:−
We know that,
─── ❖ ── ✦ ── ❖ ───
{ \underline{ \boxed{ \black{ \sf{amount = p (1 + { \frac{r}{100} }^{n} ) }}}}}
\blackamount=p(1+
100
r
n
)
Where,
↠P(principal) = ₹1,600
↠R(rate) = 5%.
↠ N(time) = 3years.
Note :
As it is compounded half yearly therefore, rate is divided by 2 and time is 3 years.
❥ Procedure :
Substituting the given values as follows :
\begin{gathered} \dashrightarrow \sf \: a = 1600(1 + { \frac{ \cancel5}{ \cancel{100}} )}^{3} \\ \dashrightarrow \sf \: a = 1600 \times (1 + \frac{1}{20} {)}^{3} \\ \dashrightarrow \sf \: a = 16 \cancel {00} \times \frac{21}{20} \times \frac{21}{2 \cancel 0} \times \frac{21}{\cancel{20}} \\ \dashrightarrow \sf \: a = 178.2 \end{gathered}
⇢a=1600(1+
100
5
)
3
⇢a=1600×(1+ 201 ) 3⇢a=16
00 × 2021 × 2 0
21 × 20/21⇢a=178.2
Principe
We also know that :
↠ C. I. = Amount - Principal
↠ C. I. = 1768.2 - 1,600
↠ C. I. = 168.2
\mathfrak{\huge{\purple{\underline{\underline{Hence}}}}}
Hence
Answer is 168.2
Answer:
I = P [(1 + R%/n)^nt − 1]
Data: P - Principal, R% - Rate of Interest- 10%, n- frequency of compounding in a year-2, t- number of years- 1.5 years.
I = 16000 [(1 + 10%/2)^2 × 1.5 − 1]
I = 16000 [(1.05)^3 − 1]
I = 16000 [1.1576 − 1]
I = 16000 × 0.1576
I = 2522
Hope it helps you!!