Question

Jaya borrowed ₹ 50000 for 2 years. The rates of interest for two successive years are 12% and 15% respectively. She repays ₹ 33000 at the end of the first year. Find the amount she must pay at the end of the second year to clear her debt.​

Answer 1

Step-by-step explanation:

Given :

• Principal = Rs. 50000
• Time = 2 years
• Rate of interest = 12%

To find :

• Amount she must pay at the end of the second year to clear her debt

Formula being use :

${\bold{: \: ⟹ \: \: \: \: \: \: \: \: \: \: }}{\bold{\underline{\boxed{\rm{Amount = P {\Big(1 + \frac{R}{100}\Big)}^{n}}}}}}$

Where,

• P is principal
• R is rate of interest
• n is no. of years

Solution :

${\bold{⟼ \: \: \: \: \: \: }}{\bold{\sf{Amount_{(after \: 1st \: year)} = }}}{\bold{\rm{\: \: P \Big(1 + \frac{R}{100}\Big)}}}$

${\bold{⟼ \: \: \: \: \: \: }}{\bold{\sf{Amount_{(after \: 1st \: year)} \: = }}}{\bold{\rm{\: \: 50000\Big(1 + \frac{12}{100}\Big)}}}$

${\bold{⟼ \: \: \: \: \: \: }}{\bold{\sf{Amount_{(after \: 1st \: year)}= }}}{\bold{\rm{\: \: 50000 × \frac{112}{100}}}}$

${\bold{⟼ \: \: \: \: \: \: }}{\large{\boxed{\rm{\red{Amount_{(after \: 1st \: year)} \: = Rs. 56000 }}}}}$

❍ As per the given question,

Amount paid at the end of 1st year = Rs. 33000

❍ It means that the principal for the 2nd year is the difference between the amount for 1st year and the amount of money paid at the end of 1st year

Therefore,

➠ Principal for 2nd year = Rs. ( 56000 - 33000)

ㅤ= Rs. 23000

➠ Time = 1 year

➠ Rate = 15%

${\bold{⟼ \: \: \: \: \: \: }}{\bold{\sf{Amount_{(due \: after \: 2nd \: year)} \: = \: }}}{\bold{\rm{\: \: P {\Big(1 + \frac{R}{100}{\Big)}}}}}$

${\bold{⟼ \: \: \: \: \: \: }}{\bold{\sf{Amount_{(due \: after \: 2nd \: year)}= \: }}}{\bold{\rm{\: \: 23000 {\Big(1 + \frac{15}{100}{\Big)}}}}}$

${\bold{⟼ \: \: \: \: \: \: }}{\bold{\sf{Amount_{(due \: after \: 2nd \: year)}= \: }}}{\bold{\rm{\: \: 23000 × \frac{115}{100}}}}$

${\bold{⟼ \: \: \: \: \: \: \: \: \: \: \: \: }}{\bold{\boxed{\boxed{\mathfrak{\orange{Rs. 26450}}}}}}$

Hence, Jaya has to pay Rs. 26450 at the end on 2nd year to clear her debt