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a loan of 10000is to be paid back in 30 equal installments the amount of each installment to cover the principal and at 4%pa.a CI
? Related: Time Value of Money (Part - 3)
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a loan of 10000is to be paid back in 30 equal installments the amount...
Understanding the Loan Structure
To calculate the equal installments for a loan of $10,000 to be repaid in 30 equal installments at an interest rate of 4% per annum compounded annually, we can use the formula for the Equated Monthly Installment (EMI).
Formula for EMI Calculation
The formula for calculating EMI is:
\[ EMI = P \times \frac{r(1 + r)^n}{(1 + r)^n - 1} \]
Where:
- P = Principal amount ($10,000)
- r = Monthly interest rate (annual rate / 12)
- n = Total number of installments (30)
Calculating Monthly Interest Rate
- Convert the annual interest rate to a monthly rate:
\[ r = \frac{4\%}{12} = \frac{0.04}{12} \approx 0.003333 \]
Calculating Total Installments
- The total number of installments is 30.
Substituting into the EMI Formula
- Plugging in the values:
\[ EMI = 10000 \times \frac{0.003333(1 + 0.003333)^{30}}{(1 + 0.003333)^{30} - 1} \]
- This can be calculated to find the EMI.
Final Calculation
- After calculating the above formula, you will find that the monthly installment (EMI) amounts to approximately $368.33.
Conclusion
- The total amount paid back over 30 months will be:
\[ Total Payment = EMI \times n = 368.33 \times 30 \approx 11,050 \]
- Thus, the borrower will pay approximately $11,050 over the term of the loan, which includes the principal and the interest.
To calculate the equal installments for a loan of $10,000 to be repaid in 30 equal installments at an interest rate of 4% per annum compounded annually, we can use the formula for the Equated Monthly Installment (EMI).
Formula for EMI Calculation
The formula for calculating EMI is:
\[ EMI = P \times \frac{r(1 + r)^n}{(1 + r)^n - 1} \]
Where:
- P = Principal amount ($10,000)
- r = Monthly interest rate (annual rate / 12)
- n = Total number of installments (30)
Calculating Monthly Interest Rate
- Convert the annual interest rate to a monthly rate:
\[ r = \frac{4\%}{12} = \frac{0.04}{12} \approx 0.003333 \]
Calculating Total Installments
- The total number of installments is 30.
Substituting into the EMI Formula
- Plugging in the values:
\[ EMI = 10000 \times \frac{0.003333(1 + 0.003333)^{30}}{(1 + 0.003333)^{30} - 1} \]
- This can be calculated to find the EMI.
Final Calculation
- After calculating the above formula, you will find that the monthly installment (EMI) amounts to approximately $368.33.
Conclusion
- The total amount paid back over 30 months will be:
\[ Total Payment = EMI \times n = 368.33 \times 30 \approx 11,050 \]
- Thus, the borrower will pay approximately $11,050 over the term of the loan, which includes the principal and the interest.
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a loan of 10000is to be paid back in 30 equal installments the amount of each installment to cover the principal and at 4%pa.a CI Related: Time Value of Money (Part - 3)?
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a loan of 10000is to be paid back in 30 equal installments the amount of each installment to cover the principal and at 4%pa.a CI Related: Time Value of Money (Part - 3)? for CA CPT 2025 is part of CA CPT preparation. The Question and answers have been prepared according to the CA CPT exam syllabus. Information about a loan of 10000is to be paid back in 30 equal installments the amount of each installment to cover the principal and at 4%pa.a CI Related: Time Value of Money (Part - 3)? covers all topics & solutions for CA CPT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for a loan of 10000is to be paid back in 30 equal installments the amount of each installment to cover the principal and at 4%pa.a CI Related: Time Value of Money (Part - 3)?.
a loan of 10000is to be paid back in 30 equal installments the amount of each installment to cover the principal and at 4%pa.a CI Related: Time Value of Money (Part - 3)? for CA CPT 2025 is part of CA CPT preparation. The Question and answers have been prepared according to the CA CPT exam syllabus. Information about a loan of 10000is to be paid back in 30 equal installments the amount of each installment to cover the principal and at 4%pa.a CI Related: Time Value of Money (Part - 3)? covers all topics & solutions for CA CPT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for a loan of 10000is to be paid back in 30 equal installments the amount of each installment to cover the principal and at 4%pa.a CI Related: Time Value of Money (Part - 3)?.
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