Question

Find the present value of an ordinary annuity of Rs.42000 p.a. for 4 years at 14% p.a. compounded annually​

Answer 1

$\large {\dag \; {\underline{\underline{\green{\pmb{\textbf{\textsf{ \; Solution :- }}}}}}}}$

Principal = RS.42000

Rate Of Interest = 14 %

Number s of time / Years = 4 years

Formulae Using :-

$\begin{gathered}\boxed{\tt{ \: \: Amount \: = \: p \: {\bigg[1 + \dfrac{r}{100} \bigg]}^{n} \: \: }} \\ \end{gathered}$

Where , P is principal , r is rate of interest ,n is number of years or time.

$\begin{gathered}\boxed{\rm{ Compound Interest = A-P}} \\ \end{gathered}$

Where A is Amount or P is principal .

Amount :-

$\rm \: \: Amount \: = \: 42000 \: {\bigg[1 + \dfrac{14}{100} \bigg]} {}^{4}$

$\rm \: \: Amount \: = \: 42000 \: {\bigg[\dfrac{100 + 14}{100} \bigg]} {}^{4}$

$\rm \: \: Amount \: = \: 42000 \: {\bigg[\dfrac{1 14}{100} \bigg]} \times {\bigg[\dfrac{1 14}{100} \bigg]} \times {\bigg[\dfrac{1 14}{100} \bigg]} \times {\bigg[\dfrac{1 14}{100} \bigg]}$

$\rm \: \: Amount \: =47880$

Compound Interest =

Amount - principal

$47880 - 42000 \\ = 5880$

The Amount =₹ 47880

Compound Interest =₹ 5880

More Formulae =

$\begin{gathered}\begin{gathered}\: \: \: \: \: \: \begin{gathered}\begin{gathered} \footnotesize{\boxed{ \begin{array}{cc} \small\underline{\frak{\pmb{ \red{More \: Formulae}}}} \\ \\ \bigstar \: \bf{P = \dfrac{SI \times 100}{r \times n} }\\ \\ \bigstar \: \bf{r = \dfrac{SI \times 100}{P \times n} }\\ \\ \bigstar \: \bf{n = \dfrac{SI \times 100}{P \times r} }\\ \\ \bigstar \: \bf{Amount = P\bigg(\dfrac{100 + rn}{100} \bigg) }\: \end{array} }}\end{gathered}\end{gathered}\end{gathered}\end{gathered}$