Question

find the amount and the compound interest of $ 64,000 in 1 1/2 year at 5 percent p.a.,when the interest is compounded annually​

Answer 1

AnswEr :

$\bf{Compound\:interest}\textsf{ is calculated on the} \\ \textsf{principal amount and also on the accumulated} \\ \textsf{interest of previous periods, and can thus be} \\ \textsf{regarded as \bf{interest on interest.}}$

$\textsf{But, Here we won't use the Formula of} \\ \textsf{Compound Interest. we will use Simple}\\ \textsf{Interest Formula Only.}\\\\\bullet\:\:\textsf{Interest on First Year of Simple Interest}\\ \quad\textsf{and Compound Interest are always equal.}\\\\\bullet \: \: \textsf{Principal for Compound Interest for next}\\\quad\textsf{consecutive years can be find by Adding}\\ \quad\textsf{Principal and Past Year Interest}$

$\rule{100}{2}$

$\bf\dag \:\underline{\large{\textit{Year 1 :}}}$

$\bf{we\:have}\begin{cases}\sf{Principal=Rs.\:64000}\\\sf{Time=1 \:year}\\ \sf{Rate=5\% \:p.a.}\end{cases}$

$:\implies \sf Interest = \dfrac{Principal \times Rate\times Time}{100} \\ \\\\:\implies \sf Interest = \dfrac{Rs. \:64000 \times 5 \times 1}{100} \\ \\ \\:\implies \sf Interest = \cancel\dfrac{Rs.\:320000}{100} \\ \\ \\:\implies \green{\sf Interest = Rs.\:3200}$

$\rule{200}{1}$

$\bf\dag \:\underline{\large{\textit{Year 2 :}}}$

$\bf{we\:have}\begin{cases}\sf{Principal=Rs. \:(64000 + 3200)}\\ \qquad \qquad\sf{= Rs.\:67200}\\\sf{Time=\dfrac{1}{2} \:year}\\\sf{Rate=5\% \:p.a.}\end{cases}$

$:\implies \sf Interest = \dfrac{Principal \times Rate\times Time}{100} \\ \\\\:\implies \sf Interest = \dfrac{Rs. \:67200\times 5 \times \dfrac{1}{2} }{100} \\ \\ \\:\implies \sf Interest = \cancel\dfrac{Rs.\:336000}{200} \\ \\ \\:\implies \green{\sf Interest = Rs.\:1680}$

$\rule{200}{2}$

• TOTAL⠀COMPOUND⠀INTEREST :

↠ Compound Interest = Year 1 + Year 2

↠ Compound Interest = Rs.(3200 + 1680)

↠ Compound Interest = Rs. 4880

⠀

∴ Compound Interest will be Rs. 4880.