Question

Mastram borrows rupees 20000 for 2 years compounded annually the rate of interest for two successive years at 9% and 10% respectively if he repays rupees 1200 at the end of the first year and Rupees 1660 at the end of the second year find the amount outstanding at the beginning of the third year​

Answer 1

Answer:

Amount outstanding at the beginning of third year is Rs 21,120 .

Step-by-step explanation:

Given as :

The borrows principal = p = rs 20,000

The time period = t = 2 years compounded annually

The successive rate of interest are 9% and 10%

Let The Amount paid after 2 years = Rs A

The Amount paid at the end of first year = rs 1200

The Amount paid at the end of second year = rs 1660

Let The Amount outstanding at the beginning of third year =Rs A'

According to question

From Compound Interest method

Amount = Principal × $(1+\dfrac{\textrm rate}{100})^{\textrm time}$

Or, A = p  × $(1+\dfrac{\textrm r}{100})^{\textrm t}$

Here the rate is for two successive years

So, A = Rs 20,000 × $(1+\dfrac{\textrm 9}{100})^{\textrm 1}$ × $(1+\dfrac{\textrm 10}{100})^{\textrm 1}$

or, A =  Rs 20,000 × 1.09 × 1.1

∴ Amount = Rs 23,980

So, The Amount after 2 years at successive rate = A = rs 23,980

Again

∵ Mr, Mastram paid Rs 1200 at the end of first year

and rs 1660 at the end of second year

So. Amount outstanding at the beginning of third year = Amount after 2 years at successive rate - (Paid amount at the end of first year + Paid amount at the end of first year)

Or, A' = Rs 23,980 - (rs 1200 + rs 1660)

Or, A' = Rs 23,980 - (Rs 2860)

Or, A' = Rs 21,120

So,  Amount outstanding at the beginning of third year = A' = Rs 21,120

Hence, Amount outstanding at the beginning of third year is Rs 21,120 . Answer