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A sum of 10000 is borrowed at 8% p.a. compound annually which is which is paid back in 3 equal annual instalments. what is the amount of each instalments?
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A sum of 10000 is borrowed at 8% p.a. compound annually which is which...
Understanding the Loan Repayment Structure
To determine the amount of each annual installment for a loan of 10,000 at an 8% annual compound interest rate, paid back in 3 equal installments, we can use the formula for the present value of an annuity.
Present Value of Annuity Formula
The formula to calculate the present value \( PV \) of an annuity is given by:
\[
PV = P \times \left( \frac{1 - (1 + r)^{-n}}{r} \right)
\]
Where:
- \( PV \) = Present Value (loan amount)
- \( P \) = Annual installment amount
- \( r \) = Annual interest rate (in decimal)
- \( n \) = Number of installments
Given Values
- Loan Amount \( PV = 10,000 \)
- Interest Rate \( r = 0.08 \)
- Number of Installments \( n = 3 \)
Rearranging the Formula
We need to find \( P \):
\[
10,000 = P \times \left( \frac{1 - (1 + 0.08)^{-3}}{0.08} \right)
\]
Calculating the factor:
1. Calculate \( (1 + 0.08)^{-3} \):
\[
(1.08)^{-3} \approx 0.7938
\]
2. Substitute in the annuity formula:
\[
10,000 = P \times \left( \frac{1 - 0.7938}{0.08} \right)
\]
\[
10,000 = P \times \left( \frac{0.2062}{0.08} \right) \approx P \times 2.5775
\]
3. Solve for \( P \):
\[
P = \frac{10,000}{2.5775} \approx 3872.13
\]
Final Amount of Each Installment
The amount of each annual installment is approximately **3,872.13**.
To determine the amount of each annual installment for a loan of 10,000 at an 8% annual compound interest rate, paid back in 3 equal installments, we can use the formula for the present value of an annuity.
Present Value of Annuity Formula
The formula to calculate the present value \( PV \) of an annuity is given by:
\[
PV = P \times \left( \frac{1 - (1 + r)^{-n}}{r} \right)
\]
Where:
- \( PV \) = Present Value (loan amount)
- \( P \) = Annual installment amount
- \( r \) = Annual interest rate (in decimal)
- \( n \) = Number of installments
Given Values
- Loan Amount \( PV = 10,000 \)
- Interest Rate \( r = 0.08 \)
- Number of Installments \( n = 3 \)
Rearranging the Formula
We need to find \( P \):
\[
10,000 = P \times \left( \frac{1 - (1 + 0.08)^{-3}}{0.08} \right)
\]
Calculating the factor:
1. Calculate \( (1 + 0.08)^{-3} \):
\[
(1.08)^{-3} \approx 0.7938
\]
2. Substitute in the annuity formula:
\[
10,000 = P \times \left( \frac{1 - 0.7938}{0.08} \right)
\]
\[
10,000 = P \times \left( \frac{0.2062}{0.08} \right) \approx P \times 2.5775
\]
3. Solve for \( P \):
\[
P = \frac{10,000}{2.5775} \approx 3872.13
\]
Final Amount of Each Installment
The amount of each annual installment is approximately **3,872.13**.
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A sum of 10000 is borrowed at 8% p.a. compound annually which is which is paid back in 3 equal annual instalments. what is the amount of each instalments?
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A sum of 10000 is borrowed at 8% p.a. compound annually which is which is paid back in 3 equal annual instalments. what is the amount of each instalments? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A sum of 10000 is borrowed at 8% p.a. compound annually which is which is paid back in 3 equal annual instalments. what is the amount of each instalments? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A sum of 10000 is borrowed at 8% p.a. compound annually which is which is paid back in 3 equal annual instalments. what is the amount of each instalments?.
A sum of 10000 is borrowed at 8% p.a. compound annually which is which is paid back in 3 equal annual instalments. what is the amount of each instalments? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A sum of 10000 is borrowed at 8% p.a. compound annually which is which is paid back in 3 equal annual instalments. what is the amount of each instalments? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A sum of 10000 is borrowed at 8% p.a. compound annually which is which is paid back in 3 equal annual instalments. what is the amount of each instalments?.
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