Question

If the interest is₹76.50, time is 9 months and compound rate of interest is 6% p.a. compounded
quarterly, find the principal. ​

Answer 1

Given:

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

${\underline{\mathbb{ As \; we \; know \; that \dag}}}$

$\;\;\;\;\;\;\;\;\;\dag \;\; \bigg [\bf Compound \; Interest = P\bigg( 1 + \frac{r}{400} \bigg)^{4n} - 1 \bigg]$

→here,

C.I = 76.50

Rate = 9%

time =  9 months

→Substituting we get,

$\implies \sf 76.50 = P \bigg[\bigg( 1 + \dfrac{9}{400} \bigg) ^{3} - 1 \bigg]$

$\implies \sf 76.50 = P \bigg[\bigg( \dfrac{409}{400} \bigg)^{3} - 1 \bigg]$

$\implies \sf 76.50 = P \bigg[\bigg( \dfrac{409}{400} \bigg)^{3} - 1 \bigg]$

$\implies \sf 76.50 = P \bigg[\bigg( \dfrac{409}{400} \bigg)^{3} - 1 \bigg]$

$\implies \sf 76.50 = P \times 1.06 - 1$

$\implies \sf P = 1.06 - 1 \div 76.5$

$\implies \sf P = 1.06 - 0.01$

$\implies \sf {\boxed{\pmb{\mathtt{ P= 1.05}}}}$

• Hence the principal amount is 1.05.

$\huge\fbox{\pink{\underline{♥Thank \: You♥}}}$

Answer 2

Given:

• 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

${\underline{\frak{ As \; we \; know \; that \dag}}}$

$\;\;\;\;\;\;\;\;\;\dag \;\; \bigg [\bf Compound \; Interest = P\bigg( 1 + \frac{r}{400} \bigg)^{4n} - 1 \bigg]$

➳ here,

• C.I = 76.50
• Rate = 6%
• time =  9 months

➝ Substituting we get,

$\implies \sf p+ 76.5 = P \bigg[\bigg( 1 + \dfrac{6}{400} \bigg) ^{3} \bigg]$

$\implies \sf 76.50 = P \bigg[\bigg( \dfrac{406}{400} \bigg)^{3} - p \bigg]$

$\implies \sf 76.50 = P \times 1.0458 - p$

$\implies \sf 76.50 = P ( 1.0458 - 1 )$

$\implies \sf 76.50 = P \times 0.0458$

$\implies \sf P = 76.5 \div 0.0458$

$\implies \sf {\boxed{\pmb{\frak{ P= 1670.30}}}}$

• henceforth thee principal amount is 1.03