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X Bank offers you housing loan at an interest rate of 8% compounded quarterly.
a. Determine the effective annual interest of the loan.
b. If Y Bank offers you the same loan at 8.15% compounded annually, which one would you prefer?
a. Determine the effective annual interest of the loan.
b. If Y Bank offers you the same loan at 8.15% compounded annually, which one would you prefer?
Most Upvoted Answer
X Bank offers you housing loan at an interest rate of 8% compounded qu...
Effective Annual Interest Rate Calculation
To determine the effective annual interest rate (EAR) for X Bank's loan, we use the formula for compounding:
- EAR = (1 + r/n)^(n*t) - 1
Where:
- r = nominal interest rate (8% or 0.08)
- n = number of compounding periods per year (4 for quarterly)
- t = number of years (1 for annual calculation)
Plugging in the values:
- EAR = (1 + 0.08/4)^(4*1) - 1
- EAR = (1 + 0.02)^4 - 1
- EAR = (1.02)^4 - 1
- EAR ≈ 0.082432 - 1
- EAR ≈ 0.0824 or 8.24%
Comparison with Y Bank's Offer
- Y Bank offers a nominal interest rate of 8.15% compounded annually, which is simply 8.15% for the year.
Preference Analysis
- X Bank: Effective annual interest rate is 8.24%
- Y Bank: Effective annual interest rate is 8.15%
Decision
- Lower Rate: Y Bank has a lower effective annual interest rate (8.15%) compared to X Bank (8.24%).
- Overall Cost: Choosing Y Bank would mean lower total interest payments over the life of the loan.
- Flexibility & Options: While X Bank offers quarterly compounding, the higher effective interest rate makes it less attractive.
Conclusion
Based on the effective annual rates, it is advisable to prefer Y Bank's offer as it results in lower total interest costs, making it a more economical choice for your housing loan.
To determine the effective annual interest rate (EAR) for X Bank's loan, we use the formula for compounding:
- EAR = (1 + r/n)^(n*t) - 1
Where:
- r = nominal interest rate (8% or 0.08)
- n = number of compounding periods per year (4 for quarterly)
- t = number of years (1 for annual calculation)
Plugging in the values:
- EAR = (1 + 0.08/4)^(4*1) - 1
- EAR = (1 + 0.02)^4 - 1
- EAR = (1.02)^4 - 1
- EAR ≈ 0.082432 - 1
- EAR ≈ 0.0824 or 8.24%
Comparison with Y Bank's Offer
- Y Bank offers a nominal interest rate of 8.15% compounded annually, which is simply 8.15% for the year.
Preference Analysis
- X Bank: Effective annual interest rate is 8.24%
- Y Bank: Effective annual interest rate is 8.15%
Decision
- Lower Rate: Y Bank has a lower effective annual interest rate (8.15%) compared to X Bank (8.24%).
- Overall Cost: Choosing Y Bank would mean lower total interest payments over the life of the loan.
- Flexibility & Options: While X Bank offers quarterly compounding, the higher effective interest rate makes it less attractive.
Conclusion
Based on the effective annual rates, it is advisable to prefer Y Bank's offer as it results in lower total interest costs, making it a more economical choice for your housing loan.
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X Bank offers you housing loan at an interest rate of 8% compounded quarterly.a. Determine the effective annual interest of the loan.b. If Y Bank offers you the same loan at 8.15% compounded annually, which one would you prefer?
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