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A man borrows 10000 rupees at 20 % compound interest for 3 years. If every year he pays 2000 rupees as repayment. How much amount is still left to be paid by the man?
- a)5000
- b)7000
- c)9000
- d)10000
- e)None of these
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
A man borrows 10000 rupees at 20 % compound interest for 3 years. If e...
Amount to be paid at the end of three years = 10000*(1+20/100)3 = 17280
Amount paid as instalment by the man = 2000*(1+20/100)2 + 2000*(1+20/100) + 2000 = 7280
So remaining amount = 10000
Amount paid as instalment by the man = 2000*(1+20/100)2 + 2000*(1+20/100) + 2000 = 7280
So remaining amount = 10000
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A man borrows 10000 rupees at 20 % compound interest for 3 years. If e...
To solve this problem, we need to calculate the compound interest for 3 years and subtract the repayment amount from the borrowed amount.
Step 1: Calculate the compound interest
The compound interest formula is given by:
A = P(1 + r/n)^(nt)
Where:
A = the final amount (including interest)
P = the principal amount (borrowed amount)
r = annual interest rate (in decimal form)
n = number of times interest is compounded per year
t = time in years
Given:
P = 10000 rupees
r = 20% = 0.20 (converted to decimal)
n = 1 (compounded annually)
t = 3 years
Using the compound interest formula:
A = 10000(1 + 0.20/1)^(1*3)
A = 10000(1 + 0.20)^3
A = 10000(1.20)^3
A = 10000(1.728)
A = 17280 rupees
Step 2: Calculate the remaining amount to be paid
The man repays 2000 rupees every year for 3 years.
Total repayment = 2000 * 3 = 6000 rupees
Remaining amount to be paid = A - Total repayment
Remaining amount = 17280 - 6000
Remaining amount = 11280 rupees
Therefore, the amount still left to be paid by the man is 11280 rupees, which corresponds to option 'D'.
Step 1: Calculate the compound interest
The compound interest formula is given by:
A = P(1 + r/n)^(nt)
Where:
A = the final amount (including interest)
P = the principal amount (borrowed amount)
r = annual interest rate (in decimal form)
n = number of times interest is compounded per year
t = time in years
Given:
P = 10000 rupees
r = 20% = 0.20 (converted to decimal)
n = 1 (compounded annually)
t = 3 years
Using the compound interest formula:
A = 10000(1 + 0.20/1)^(1*3)
A = 10000(1 + 0.20)^3
A = 10000(1.20)^3
A = 10000(1.728)
A = 17280 rupees
Step 2: Calculate the remaining amount to be paid
The man repays 2000 rupees every year for 3 years.
Total repayment = 2000 * 3 = 6000 rupees
Remaining amount to be paid = A - Total repayment
Remaining amount = 17280 - 6000
Remaining amount = 11280 rupees
Therefore, the amount still left to be paid by the man is 11280 rupees, which corresponds to option 'D'.
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