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Class 11

>>Applied Mathematics

>>Basics of financial mathematics

>>Accumulation with simple and compound interest

>>Find the amount and the compound interes

Question

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Find the amount and the compound interest on 50000 for 1

2

1

years at 8% per annum with the interest being compounded semi- annually.

Medium

Updated on : 2022-09-05

Solution

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It is given that

Principal (P) = 50000

Rate of interest (r) = 8% p.a. = 4% semi-annually

Period (n)= 1

2

1

years = 3 semi-annually

We know that

Amount = P(1+r/100)

n

Substituting the values

= 50000(1+4/100)

3

By further calculation

= 50000(26/25)

3

= 50000×26/25×26/25×26/25

= 56243.20

Here

Compound interest = A - P

Substituting the values

= 56243.20−50000

= 6243.20 .

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[tex]\underline{\bf{Question:-}}[/tex]

Find compound interest on ₹ 50000 for 2 years and 8 months at 30% per annum compounded annually.

[tex]\underline{\bf{Given\:that:-}}[/tex]

▶️Principle, p = 50, 000

▶️Time period, n = 2 yrs + 8 months

▶️Rate of interest, r = 30 % per annum.

[tex]\underline{\bf{Equation\:used:-}}[/tex]

[tex]\sf{:\implies{Compound\:Interest = P(1+\dfrac{r}{n})^{nt}-1}}[/tex]

[tex]\underline{\bf{Solution:-}}[/tex]

We know,

[tex]\sf{:\implies{Compound\:Interest = P(1+\dfrac{r}{n})^{nt}-1}}[/tex]

[tex]\sf{:\implies{CI = 50,000(1+\dfrac{30}{100})^{\dfrac{8}{3}}-1}}[/tex]

[tex]\sf{:\implies{CI = 50,000(1+0.30)^{\dfrac{8}{3}}-1}}[/tex]

[tex]\sf{:\implies{CI = 50,000(1.30)^{\dfrac{1}{3}\:\times\:8}-1}}[/tex]

[tex]\sf{:\implies{CI = 50,000[(1.30)^{\dfrac{1}{3}\:\times\:8}-1]}}[/tex]

[tex]\sf{:\implies{(1.3)^{\dfrac{8}{3}}}=(1.3)^{\dfrac{1}{8}\:\times\:8}[/tex]= 2.013023939

[tex]\sf{:\implies{CI = 50,000[2.013023939-1]}}[/tex]

[tex]\sf{:\implies{CI = 50,000\:\times\:1.013023939}}[/tex]

[tex]\sf{:\implies{CI = \bold{50,651.196}}}[/tex]

[tex]\underline{\sf{Additional\:information:-}}[/tex]

1. Amount received on a certain sum of money of Rs P invested at the rate of r % per annum compounded annually for n years is given by

[tex]\boxed{\bf{:\implies{Amount = P(1+\dfrac{r}{n})^{nt}}}}[/tex]

2. Amount received on a certain sum of money of Rs P invested at the rate of r % per annum compounded semi - annually for n years is given by

[tex]\boxed{\bf{:\implies{Amount = P(1+\dfrac{r}{200})^{2n}}}}[/tex]

3. Amount received on a certain sum of money of Rs P invested at the rate of r % per annum compounded quarterly for n years is given by

[tex]\boxed{\bf{:\implies{Amount = P(1+\dfrac{r}{400})^{4n}}}}[/tex]

4. Amount received on a certain sum of money of Rs P invested at the rate of r % per annum compounded monthly for n years is given by

[tex]\boxed{\bf{:\implies{Amount = P(1+\dfrac{r}{1200})^{12n}}}}[/tex]