If the interest is₹76.50, time is 9 months and compound rate of interest is 6% p.a. compounded
quarterly, find the principal.
Answers
Hope this Will Help You
☆Solution☆
Here, P = $320,000, R = 20% p.a. and n = 1 year.
∴ Amount after 1 year = P ( 1 + R/4 ) 4n
= 320,000 x ( 1 + 0.20/4 ) 4 x 1
= 320,000 x ( 1 + 0.05) 4
= 320,000 x (1.05 ) 4
= 320,000 x 1.21550
= Rs. 388,962
∴ Compound interest = 388,962 – 320,000 = 68,962
Final Answer:
68,982
Thanks !
Answer:
The interest is ₹76.50, time is 9 months and compound rate of interest is 6% p.a. quarterly
To Find:
The principal amount
Solution
➝ Here as we have given the compound interest the rate of interest and the time let us find the principal using suitable formulae
{\underline{\mathbb{ As \; we \; know \; that \dag}}}
Asweknowthat†
\;\;\;\;\;\;\;\;\;\dag \;\; \bigg [\bf Compound \; Interest = P\bigg( 1 + \frac{r}{400} \bigg)^{4n} - 1 \bigg]†[CompoundInterest=P(1+
400
r
)
4n
−1]
→here,
C.I = 76.50
Rate = 9%
time = 9 months
→Substituting we get,
\implies \sf 76.50 = P \bigg[\bigg( 1 + \dfrac{9}{400} \bigg) ^{3} - 1 \bigg]⟹76.50=P[(1+
400
9
)
3
−1]
\implies \sf 76.50 = P \bigg[\bigg( \dfrac{409}{400} \bigg)^{3} - 1 \bigg]⟹76.50=P[(
400
409
)
3
−1]
\implies \sf 76.50 = P \bigg[\bigg( \dfrac{409}{400} \bigg)^{3} - 1 \bigg]⟹76.50=P[(
400
409
)
3
−1]
\implies \sf 76.50 = P \bigg[\bigg( \dfrac{409}{400} \bigg)^{3} - 1 \bigg]⟹76.50=P[(
400
409
)
3
−1]
\implies \sf 76.50 = P \times 1.06 - 1⟹76.50=P×1.06−1
\implies \sf P = 1.06 - 1 \div 76.5⟹P=1.06−1÷76.5
\implies \sf P = 1.06 - 0.01⟹P=1.06−0.01
\implies \sf {\boxed{\pmb{\mathtt{ P= 1.05}}}}⟹
P=1.05
P=1.05
Hence the principal amount is