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A man borrows Rs. 3000 at the rate of 10% compounded annually. At the end of each year, he pays back Rs. 1000. How much amount should he pay at the end of the 3rd year to clear all his dues?
- a)Rs. 1583
- b)Rs. 1789
- c)Rs. 1600
- d)Rs. 1683
- e)None of these
Correct answer is option 'D'. Can you explain this answer?
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A man borrows Rs. 3000 at the rate of 10% compounded annually. At the ...
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A man borrows Rs. 3000 at the rate of 10% compounded annually. At the ...
Given:
Principal amount (P) = Rs. 3000
Rate of interest (R) = 10% compounded annually
Amount paid at the end of each year = Rs. 1000
To find: Amount to be paid at the end of the third year to clear all dues
Solution:
Let us first calculate the interest for 3 years using the compound interest formula:
A = P(1 + R/100)^n
Where A is the amount, P is the principal, R is the rate of interest, and n is the number of years.
After 1 year, the amount becomes:
A1 = 3000(1 + 10/100)^1 = Rs. 3300
He pays Rs. 1000 at the end of the year, so the amount left after 1 year is:
P1 = A1 - 1000 = Rs. 2300
After 2 years, the amount becomes:
A2 = 2300(1 + 10/100)^1 = Rs. 2530
He pays Rs. 1000 at the end of the year, so the amount left after 2 years is:
P2 = A2 - 1000 = Rs. 1530
After 3 years, the amount becomes:
A3 = 1530(1 + 10/100)^1 = Rs. 1683
Therefore, the amount to be paid at the end of the 3rd year to clear all dues is Rs. 1683.
Hence, the correct option is (d) Rs. 1683.
Principal amount (P) = Rs. 3000
Rate of interest (R) = 10% compounded annually
Amount paid at the end of each year = Rs. 1000
To find: Amount to be paid at the end of the third year to clear all dues
Solution:
Let us first calculate the interest for 3 years using the compound interest formula:
A = P(1 + R/100)^n
Where A is the amount, P is the principal, R is the rate of interest, and n is the number of years.
After 1 year, the amount becomes:
A1 = 3000(1 + 10/100)^1 = Rs. 3300
He pays Rs. 1000 at the end of the year, so the amount left after 1 year is:
P1 = A1 - 1000 = Rs. 2300
After 2 years, the amount becomes:
A2 = 2300(1 + 10/100)^1 = Rs. 2530
He pays Rs. 1000 at the end of the year, so the amount left after 2 years is:
P2 = A2 - 1000 = Rs. 1530
After 3 years, the amount becomes:
A3 = 1530(1 + 10/100)^1 = Rs. 1683
Therefore, the amount to be paid at the end of the 3rd year to clear all dues is Rs. 1683.
Hence, the correct option is (d) Rs. 1683.
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A man borrows Rs. 3000 at the rate of 10% compounded annually. At the end of each year, he pays back Rs. 1000. How much amount should he pay at the end of the 3rd year to clear all his dues?a)Rs. 1583b)Rs. 1789c)Rs. 1600d)Rs. 1683e)None of theseCorrect answer is option 'D'. Can you explain this answer?
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