Question

a man borrows Rs. 18,000 at 5% p. a compound interest. If he repays Rs. 6000 at the end of first year and Rs 8000 at the end of the second year. How much he should pay at the end of 3rd year in order to clear his debt? ​

Answer 1

Answer:

For the first year  

P=Rs18,000  

N=1year

R=5 %  

We have S.I.=  

100

PNR

​  

=  

100

18,000×1×5

​  

=Rs900

And Amount at the end of first year P+S.I.=Rs18,000+Rs900=Rs18,900

Now, for the second year  

P=Rs18,900−Rs6,000=Rs12,900  

N=1year

R=5 %  

We have S.I.=  

100

PNR

​  

=  

100

12,900×1×5

​  

=Rs645

And Amount at the end of second year P+S.I.=Rs12,900+Rs645=Rs13,545

Also, for the third year  

P=Rs13,545−Rs8,000=Rs5,545  

N=1year

R=5 %  

We have S.I.=  

100

PNR

​  

=  

100

5,545×1×5

​  

=Rs277.25

And Amount at the end of third year P+S.I.=Rs5,545+Rs277.25=Rs5,822.25

Thus, at the end of the third year, amount to be paid ==Rs5,822.25 or approximately  Rs5,822

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Answer 2

The answer is 5,822.25 Rs.

Given: The amount borrowed P = 18,000

Rate of interest R = 5% per annum (at compound interest)

The amount he paid at end 1st year = 6,000

The amount he paid at end 2nd year =8,000

To find: The amount which he need to pay at end of 3rd year

Solution:

For first year

P = 18000, R = 5%  T = 1 year

As we know simple interest (I) = $\frac{PTR}{100}$  

Interest for first year = $\frac{18000(1)(5)}{100}$  = 180(5) = 900 Rs.

∴ The amount he need to pay at end of the 1st year

= 18000 + 900 = 18,900 Rs

For second year

P = 18900 - 6000 = 12900   [∵ he paid 6000 at end of the 1st year]

R = 5% and T = 1 year  

Interest for 2nd year = $\frac{12900(1)(5)}{100}$ = 129(5) = 645 Rs.      

∴ The amount he need to pay at end of the 2nd year

= 12900 + 645 = 13,545 Rs  

For third year

P = 13,545 - 8000 = 5,545   [∵ he paid 8000 at end of the 2nd year]

R = 5% and T = 1 year  

Interest for 3rd year = $\frac{5,545 (1)(5)}{100}$ = (55.45)5  = 277.25  

∴ The amount he need to pay at end of the 3rd year

= 5,545  + 277.25 = 5,822.25  Rs.

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