To calculate: The annual percentage rate and the effective annual rate of the two loans
Introduction:
Explanation of Solution
Time line of the payments:
Formula to calculate the
Note: C denotes the payments, r denotes the rate of exchange, and t denotes the period. The payment is found using the formula of the present value of annuity.
Compute the present value annuity:
Hence, the payment C is $1,276.92
Note: Using the calculated C amount in the equation of the present value of annuity and with the original amount that has to be borrowed $225,000, the r values is found.
Time line of the payments:
Formula to calculate the present value annuity:
Note: C denotes the payments, r denotes the rate of exchange, and t denotes the period.
Compute the present value annuity:
Note: To find the interest rate, it is necessary to solve the equation using a spreadsheet.
Compute the interest rate using the spreadsheet:
Step 1:
- Type the formula of the present value annuity in H6 in the spreadsheet and consider the r value as H7
Step 2:
- Assume the r value as 0.10%
Step 3:
- In the spreadsheet, go to Data and select What-If-Analysis.
- Under What-If-Analysis tab, select Goal Seek
- In set cell, select H6 (the formula)
- The ‘To value’ is considered as 225,000 (the value of the present value of annuity)
- The H7 cell is selected for the 'by changing cell'.
Step 4:
- Following the previous step, click OK in the Goal Seek Status. The Goal Seek Status appears with the r value
Step 5:
- The r value appears to be 0.4579%
Hence, the r value is 0.4580%
Compute the annual percentage rate:
Note: The annual percentage rate is computed by multiplying the interest rate with the number of periods in a year.
Hence, the annual percentage rate is 5.50%
Formula to calculate the effective annual rate:
Compute the effective annual rate:
Hence, the effective annual rate is 0.0564% or 5.64%
Calculations for the nonrefundable fee:
Annual percentage rate is 5.50%
Note: The annual percentage rate for the nonrefundable fee is the quoted rate, as the fee is not considered as a part of the loan. The effective annual rate is computed with the help of the annual percentage rate.
Formula to calculate the effective annual rate:
Compute the effective annual rate:
Hence, the effective annual rate for the non-refundable fee is 0.0554% or 5.54%.
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Chapter 4 Solutions
Corporate Finance: Core Principles and Applications (Mcgraw-hill Education Series in Finance, Insurance, and Real Estate)
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