Question

Adjoining figure shows the rate of interest of 8 % per annum for car loan from AVP bank . Mr. Hegde took a loan of Rs 5,00,000 for a period of 3 years. Find the amount and interest paid by Mr. Hegde at the end of the loan period when compounded annually.​

Answer 1

$\color{red} \large \bold{Given,} \\ \\ \sf Principal\:=\:₹\:500000\:\:\:| \:\:\: Time\:=\:3\:years\:\:\:| \:\:\:Rate\:of\:Intrest\:=\:8\% \\ \\ \color{aqua} \ \bold{To \: find \: the \: amount \: and \: intrest} \\ \\ \sf Amount \: on \: a \: certain \: sum \: of \: money \: of \: P \: invested \: at \: the \: rate \: of \: r \% \: per \: \\ \sf annum \: compounded \: annually \: for \: n \: years \: is \: given \: by \: \: \color{lime} \boxed{\: \sf \: Amount\:=\:P[1\:+\: \frac{r}{100}]^n} \\ \\ \large\: \text{Substituting\:the\:values,\:we\:get,} \\ \\ \sf \: Amount\:=\:500000 \left[ 1\:+\: \frac{8}{100} \right]^3 \\ \\ \sf \: Amount\:=\:500000 \: \times \: 1.259712 \\ \\ \color{gold} \sf { \underline{Amount\:=\:₹\:629856}} \\ \\ \color{olive} \boxed{ \sf \: Intrest\:=\: Amount\:-\: Principal} \\ \\ \sf \: Intrest\:=\:629856 \: - \: 500000 \\ \\ \color{skyblue}\sf \:{ \underline{ Intrest\:=\:₹\:129856}} \\ \\ \sf \: At\:the\:end\:Mr.\:Hegde \: will \: pay \: ₹\:629856 \: as \: amount \: and \: ₹\:129856 \: as \: intrest.$

$\color{silver}\rule{200000000 pt}{2pt}$

$\color{green} \boxed{ \begin {array} { |c|c|c|} Statement&Formulas \\ \\ \\❑ \: Amount \: on \: a \: certain \: sum \: of \: money \: of \: P \: invested \: at \: the \: rate \: of \: r \% \: per \: \\ annum \: compounded \: annually \: for \: n \: years \: is \: given \: by &❑ \: Amount\:=\:P[1\:+\: \frac{r}{100}]^n \\ \\ ❑ \: Amount \: on \: a \: certain \: sum \: of \: money \: of \: P \: invested \: at \: the \: rate \: of \: r \% \: per \\ \: annum \: compounded \: quarterly \: for \: n \: years \: is \: given \: by &❑ \:Amount\:=\:P[1\:+\: \frac{r}{200}]^{4n} \\ \\ ❑ \:Amount \: on \: a \: certain \: sum \: of \: money \: of \: P \: invested \: at \: the \: rat e \: of \: r \% \: per \: \\ annum \: compounded \: monthly \: for \: n \: years \: is \: given \: b y&❑\:Amount\:=\:P\:[1\:+\: \frac{r}{1200}]^{12n} \\ \\ ❑ \:Amount\:on\:a\: certain\:sum\:of\:money\:P\:invested \:at\:a\:rate\:of\:\%\:per\:annum\: \\ compound\:semi\: annually\:for\:n\:years\:is\: given\:by &❑ \: Amount\:=\:P\: \left[ \:1\:+\: \frac{r}{200} \right]^{2n}\: \end {array}}$