What amount would become Rs.18,522 at an annual rate of interest of 10% afterone and a half years if the interest is calculated every six months?

What amount would become Rs.18,522 at an annual rate of interest of 10

1.	What amount would become Rs.18,522 at an annual rate of interest of 10% afterone and a half years if the interest is calculated every six months?
Answer» ${ \huge{ \tt{ \green{ \underline{ \underline{ QUESTION- }}}}}}$ ▪ What amount of money would become Rs. 18,522 at an annual rate of interest of 10% after one and a HALF years, if the interest is calculated every SIX months?? ${ \huge{ \tt{ \green{ \underline{ \underline{SOLUTION- }}}}}}$ ${ \blue{ \bold{<klux>GIVEN</klux>- }}}$ ${ \sf{ \pink{amount = Rs . \: 18522}}} \\ \\ { \sf{ \pink{rate = 10 \: percent}}} \\ \\{ \sf{ \pink{time = 1 \times \frac{1}{2} years = \frac{3}{2} years}}}$ ${ \bold{ \blue{TO \: FIND- }}}$ ${ \rightarrow{ \sf{principal(P)}}}$ Since, the money is COMPOUNDED half- YEARLY.. ${ \star{ \blue{ \sf{ \: \: rate \: will \: be \: halved}}}} \\ \\ { \blue{ \sf{R = \frac{10}{2} = 5 \: percent}}}$ ${ \star{ \blue{ \sf{ \: \: time \: will \: get \: doubled}}}} \\ \\ { \sf{ \blue{T = \frac{3}{2} \times 2 \: years = 3 \: years}}}$ ${ \boxed{ \boxed{ \red{ \sf{ \: \: amount = P{(1 + \frac{R}{100}) }^{T} \: \: }}}}}$ putting the above given values in the formula... ${ \sf{18522 = P {(1 + \frac{5}{100}) }^{3}}}$ ${ \implies{ \sf{18522 = P {(1 + \frac{1}{20} )}^{3}}}}$ ${ \implies{ \sf{18522 = P{( \frac{21}{20}) }^{3}}}}$ ${ \implies{ \sf{18522 = P \times \frac{9261}{8000}}}}$ ${ \implies{ \sf{P = 18522 \times \frac{8000}{9261}}}}$ ${ \implies{ \sf{P = 2 \times 8000}}}$ ${ \implies{ \boxed{ \boxed{ \pink{ \sf{P = Rs. \: 16000}}}}}}$