Question

In: Finance

If your answer does not match the answers given below, check with the instructor. There is...

If your answer does not match the answers given below, check with the instructor. There is always the chance, albeit small, that your answer is correct and there is a typo below.)

1.         Bank A offers to lend you money at 10 percent compounded monthly, Bank B at 11 percent compounded quarterly, and Bank C at 12 percent compounded annually. Calculate the effective rates and state which bank offers the lowest cost of borrowed capital.

2.         What are the interest payments on a $200 loan if the contractual rate is 12%, the loan will be paid back in four uniform interest and principal payments at the end of the next four years, and the remaining balance method of calculating interest will be used (fully amortized)? What is the actuarial, annual percentage, and the effective interest rate? (AIR, APR, ie =12%)

3.         What are the interest payments on a $1,000 loan if the contractual rate is 12%, the loan will be paid back in four uniform principal payments at the end of the next four years, and the remaining balance method of calculating interest will be used? What is the actuarial, annual percentage, and the effective interest rate? (AIR, APR, ie =12%)

4.         A farmer needs to borrow $1,000. The local PCA will make a 2‑year loan fully amortized at 10% (annual rate) with quarterly payments. A $10 loan fee and stock purchase is required. The borrower stock requirement is the lesser of $1,000 or 2% of loan principal. Assume that sufficient money is borrowed to cover the $1,000, the fee and the stock requirement. Also assume that the stock requirement is returned to borrower when the loan is paid off and the last debt payment can be reduced by the stock amount. How much money needs to be borrowed? What is the dollar amount of the stock requirement? What is the quarterly loan payment? What is the actuarial, annual percentage, and the effective interest rate? (AIR =2.83%, APR = 11.32%, ie = 11.81%)

Solutions

Expert Solution

1. computation

Bank Interest Compounding Number of period Effective Rate
A 10 Monthly 12 12.68%
B 11 Quarterly 4 12.55%
C 12 Annually 1 12.00%

So bank C offer the load at lower rate.

2. Calculation of interest payments:

Loan Amount 200
Number of Year 4
Interest Rate 12.00%
Installation (PMT Formula in Excel) 65.85

Interest payments i each years are:

Years Beg. Balance Payment Interest Repayment of principal Ending Balance
1 200 $65.85 24 $41.85 $158.15
2 $158.15 $65.85 18.98 $46.87 $111.28
3 $111.28 $65.85 13.35 $52.49 $58.79
4 $58.79 $65.85 7.06 $58.79 $0.00
Total $263.39 $63.39 $200.00 $328.23

And, effective interest rate = total interest payment / loan amount:

Overall interest Rate 31.69%
Annual Effective interest Rate/4 7.92%

3.

Loan Amount 1000
Number of Year 4
Interest Rate 12.00%
Installation (PMT Formula in Excel) 329.23
Years Beg. Balance Payment Interest Repayment of principal Ending Balance
1 1000 $329.23 120 $209.23 $790.77
2 $790.77 $329.23 94.89 $234.34 $556.42
3 $556.42 $329.23 66.77 $262.46 $293.96
4 $293.96 $329.23 35.28 $293.96 $0.00
Total $1,316.94 $316.94 $1,000.00 $1,641.15
Overall interest Rate 31.6938%
Annual Effective interest Rate/4 7.92344%

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