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A company borrows ` 10,000 on condition to repay it with compound interest at 5% p.a by annual installments of ` 1000 each. The number of years by which the debt will be clear is?
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A company borrows ` 10,000 on condition to repay it with compound inte...
Problem:
A company borrowed ` 10,000 on condition to repay it with compound interest at 5% p.a by annual installments of ` 1000 each. Find the number of years by which the debt will be cleared.
Solution:
To solve the problem, we can use the formula for the present value of an annuity due:
PV = A * ((1 - (1 + r)^-n) / r) * (1 + r)
where,
PV = present value of the annuity
A = annual payment
r = interest rate per period
n = number of periods
We know that the present value of the loan is ` 10,000 and the annual payment is ` 1000. The interest rate per period is 5% and the number of periods is what we need to find.
Step 1: Calculate the present value of the loan.
PV = ` 10,000
Step 2: Calculate the interest rate per period.
r = 5% per annum = 5/100 = 0.05
Step 3: Calculate the annual payment.
A = ` 1000
Step 4: Use the formula to find the number of periods.
PV = A * ((1 - (1 + r)^-n) / r) * (1 + r)
` 10,000 = ` 1000 * ((1 - (1 + 0.05)^-n) / 0.05) * (1 + 0.05)
` 10,000 = ` 1000 * ((1 - 1.05^-n) / 0.05) * 1.05
` 10,000 = ` 1000 * ((1 - 1.05^-n) / 0.05) * 1.05
10 = (1 - 1.05^-n) / 0.05
1.05^-n = 0.9512
n = ln(0.9512) / ln(1.05)
n = 14.21
Step 5: Round up the number of periods to the nearest integer since we cannot have fractional years.
n = 15 years
Therefore, the debt will be cleared in 15 years.
A company borrowed ` 10,000 on condition to repay it with compound interest at 5% p.a by annual installments of ` 1000 each. Find the number of years by which the debt will be cleared.
Solution:
To solve the problem, we can use the formula for the present value of an annuity due:
PV = A * ((1 - (1 + r)^-n) / r) * (1 + r)
where,
PV = present value of the annuity
A = annual payment
r = interest rate per period
n = number of periods
We know that the present value of the loan is ` 10,000 and the annual payment is ` 1000. The interest rate per period is 5% and the number of periods is what we need to find.
Step 1: Calculate the present value of the loan.
PV = ` 10,000
Step 2: Calculate the interest rate per period.
r = 5% per annum = 5/100 = 0.05
Step 3: Calculate the annual payment.
A = ` 1000
Step 4: Use the formula to find the number of periods.
PV = A * ((1 - (1 + r)^-n) / r) * (1 + r)
` 10,000 = ` 1000 * ((1 - (1 + 0.05)^-n) / 0.05) * (1 + 0.05)
` 10,000 = ` 1000 * ((1 - 1.05^-n) / 0.05) * 1.05
` 10,000 = ` 1000 * ((1 - 1.05^-n) / 0.05) * 1.05
10 = (1 - 1.05^-n) / 0.05
1.05^-n = 0.9512
n = ln(0.9512) / ln(1.05)
n = 14.21
Step 5: Round up the number of periods to the nearest integer since we cannot have fractional years.
n = 15 years
Therefore, the debt will be cleared in 15 years.
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A company borrows ` 10,000 on condition to repay it with compound interest at 5% p.a by annual installments of ` 1000 each. The number of years by which the debt will be clear is?
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A company borrows ` 10,000 on condition to repay it with compound interest at 5% p.a by annual installments of ` 1000 each. The number of years by which the debt will be clear is? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about A company borrows ` 10,000 on condition to repay it with compound interest at 5% p.a by annual installments of ` 1000 each. The number of years by which the debt will be clear is? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A company borrows ` 10,000 on condition to repay it with compound interest at 5% p.a by annual installments of ` 1000 each. The number of years by which the debt will be clear is?.
A company borrows ` 10,000 on condition to repay it with compound interest at 5% p.a by annual installments of ` 1000 each. The number of years by which the debt will be clear is? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about A company borrows ` 10,000 on condition to repay it with compound interest at 5% p.a by annual installments of ` 1000 each. The number of years by which the debt will be clear is? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A company borrows ` 10,000 on condition to repay it with compound interest at 5% p.a by annual installments of ` 1000 each. The number of years by which the debt will be clear is?.
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