find the amount and compound interest on rupees 40000 in 3 yrs at 7 1/2 p.a.

2 thoughts on “find the amount and compound interest on rupees 40000 in 3 yrs at 7 1/2 p.a.”

1. Answer:

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   P=40,000T=1 yearR=10%

   When payable quarterly,

   C.I=P(1+4×100R)4×T−P=40000(1+40010)4−40000=40000(4041)4−40000=4152.5∴C.I=Rs.4152.5

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2. Answer:

   • Amount is ₹49691.875.
   • Compound Interest is ₹9691.875.

   Step-by-step explanation:

   Given that:

   [tex]\sf{\circ\;Principal=Rs.\;40000}[/tex]

   [tex]\sf{\circ\;Rate=7\dfrac{1}{2}\%\;per\;annum}[/tex]

   [tex]\sf{\circ\;Time=3\;years}[/tex]

   To Find:

   • Amount
   • Compound Interest

   Finding amount:

   As we know that:

   [tex]\bf{\circ\;Amount=Principal\left(1+\dfrac{Rate}{100}\right)^{Time}}[/tex]

   Here,

   [tex]\sf{\circ\;Principal=Rs.\;40000}[/tex]

   [tex]\sf{\circ\;Rate=7\dfrac{1}{2}=\dfrac{15}{2}\%\;per\;annum}[/tex]

   [tex]\sf{\circ\;Time=3\;years}[/tex]

   Substituting the values,

   [tex]\sf{\longmapsto40000\left(1+\dfrac{\dfrac{15}{2}}{100}\right)^{3}}[/tex]

   [tex]\sf{\longmapsto40000\left(1+\dfrac{15}{2\times100}\right)^{3}}[/tex]

   Multiplying the denominator,

   [tex]\sf{\longmapsto40000\left(1+\dfrac{15}{200}\right)^{3}}[/tex]

   Reducing the numbers,

   [tex]\sf{\longmapsto40000\left(1+\dfrac{3}{40}\right)^{3}}[/tex]

   Adding the numbers,

   [tex]\sf{\longmapsto40000\left(\dfrac{40+3}{40}\right)^{3}}[/tex]

   [tex]\sf{\longmapsto40000\left(\dfrac{43}{40}\right)^{3}}[/tex]

   Opening the bracket,

   [tex]\sf{\longmapsto40000\times\dfrac{43}{40}\times\dfrac{43}{40}\times\dfrac{43}{40}}[/tex]

   Cutting off the zeros,

   [tex]\sf{\longmapsto40\!\!\!\not{0}\!\!\!\not{0}\!\!\!\not{0}\times\dfrac{43}{4\!\!\!\not{0}}\times\dfrac{43}{4\!\!\!\not{0}}\times\dfrac{43}{4\!\!\!\not{0}}}[/tex]

   [tex]\sf{\longmapsto40\times\dfrac{43}{4}\times\dfrac{43}{4}\times\dfrac{43}{4}}[/tex]

   Dividing the numbers,

   [tex]\sf{\longmapsto40\times10.75\times10.75\times10.75}[/tex]

   Multiplying the numbers,

   [tex]\sf{\longmapsto49691.875}[/tex]

   Hence,

   • Amount = ₹49691.875

   Now, finding compound interest:

   As we know that:

   • Compound Interest = Amount – Principal

   Here,

   • Amount = ₹49691.875
   • Principal = ₹40000

   Substituting the values,

   ↣ ₹(40000 – 49691.875)

   ↣ ₹9691.875

   Hence,

   • Compound Interest = ₹9691.875

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