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Mr. Paul borrows ₹20000 on condition to repay it with C.I. at 5% p.a in annual installments of ₹2000 each. The number of years for the debt to be paid off is?
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Mr. Paul borrows ₹20000 on condition to repay it with C.I. at 5% p.a i...
Problem: Mr. Paul borrows ₹20000 on condition to repay it with C.I. at 5% p.a in annual installments of ₹2000 each. The number of years for the debt to be paid off is?
Solution:
Step 1: Find the interest rate and installment amount
- Interest Rate (r) = 5% p.a
- Installment Amount (a) = ₹2000
Step 2: Find the amount of loan
- Let x be the number of years for the debt to be paid off
- Total amount paid by Mr. Paul = x * a = ₹2000x
- Using the formula for the future value of an annuity, we get:
FV = a * ((1 + r)^n - 1) / r
where FV is the future value, n is the number of periods, and r is the interest rate
- Substituting the values, we get:
20000 = 2000 * ((1 + 0.05)^x - 1) / 0.05
- Simplifying the equation, we get:
(1 + 0.05)^x = 1 + 20000 * 0.05 / 2000
(1 + 0.05)^x = 1.05
Step 3: Find the number of years
- Taking log on both sides, we get:
x * log(1.05) = log(1.05)
x = log(1.05) / log(1.05)
x = 1
- Therefore, the debt will be paid off in 1 year.
Conclusion: Mr. Paul will be able to pay off the debt in 1 year by making annual installments of ₹2000.
Solution:
Step 1: Find the interest rate and installment amount
- Interest Rate (r) = 5% p.a
- Installment Amount (a) = ₹2000
Step 2: Find the amount of loan
- Let x be the number of years for the debt to be paid off
- Total amount paid by Mr. Paul = x * a = ₹2000x
- Using the formula for the future value of an annuity, we get:
FV = a * ((1 + r)^n - 1) / r
where FV is the future value, n is the number of periods, and r is the interest rate
- Substituting the values, we get:
20000 = 2000 * ((1 + 0.05)^x - 1) / 0.05
- Simplifying the equation, we get:
(1 + 0.05)^x = 1 + 20000 * 0.05 / 2000
(1 + 0.05)^x = 1.05
Step 3: Find the number of years
- Taking log on both sides, we get:
x * log(1.05) = log(1.05)
x = log(1.05) / log(1.05)
x = 1
- Therefore, the debt will be paid off in 1 year.
Conclusion: Mr. Paul will be able to pay off the debt in 1 year by making annual installments of ₹2000.
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Mr. Paul borrows ₹20000 on condition to repay it with C.I. at 5% p.a in annual installments of ₹2000 each. The number of years for the debt to be paid off is?
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Mr. Paul borrows ₹20000 on condition to repay it with C.I. at 5% p.a in annual installments of ₹2000 each. The number of years for the debt to be paid off is? for CA Foundation 2025 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about Mr. Paul borrows ₹20000 on condition to repay it with C.I. at 5% p.a in annual installments of ₹2000 each. The number of years for the debt to be paid off is? covers all topics & solutions for CA Foundation 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Mr. Paul borrows ₹20000 on condition to repay it with C.I. at 5% p.a in annual installments of ₹2000 each. The number of years for the debt to be paid off is?.
Mr. Paul borrows ₹20000 on condition to repay it with C.I. at 5% p.a in annual installments of ₹2000 each. The number of years for the debt to be paid off is? for CA Foundation 2025 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about Mr. Paul borrows ₹20000 on condition to repay it with C.I. at 5% p.a in annual installments of ₹2000 each. The number of years for the debt to be paid off is? covers all topics & solutions for CA Foundation 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Mr. Paul borrows ₹20000 on condition to repay it with C.I. at 5% p.a in annual installments of ₹2000 each. The number of years for the debt to be paid off is?.
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