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

In how much time will₹ 60,000 amount to 69,257.50 at 5% per annum compound interest​

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

▶️ Principle, p = 60,000

▶️ Amount = 69,257.50

▶️ Time period, n = ?

▶️ Rate of interest, r =5 % per annum.

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

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

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

[tex]\sf{:\implies{Amount = Principle + Compound\:Interest}}[/tex]

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

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

[tex]\sf{:\implies{69,257.50 = 60,000(1+\dfrac{5}{100})^{t}}}[/tex]

[tex]\sf{:\implies{69,257.50 = 60,000(1+0.05)^{t}}}[/tex]

[tex]\sf{:\implies{69,257.50 = 60,000(1.05)^{t}}}[/tex]

[tex]\sf{:\implies{\dfrac{69,257.50}{60,000} =(1.05)^{t}}}[/tex]

[tex]\sf{:\implies{1.154291666 =(1.05)^{t}}}[/tex]

[tex]\sf{:\implies{(1.05)^3 =(1.05)^{t}}}[/tex]

[tex]\sf{:\implies{(1.05)^3 =(1.05)^{3}}}[/tex]

Therefore, the time is 3 years

[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]