A farmer needs to borrow $50,000. The local PCA will make a four year loan fully

Question

A farmer needs to borrow $50,000. The local PCA will make a four year loan fully amortized at 12% with annual payments. A $100 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 $50,000, 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 annual loan payment? What is the actuarial, annual percentage, and the effective interest rate? (AIR, APR, ie = 12.44%)


How much does the borrower need to borrow in order to cover money needed, stock and loan fee?
A. $16,824
B. $51,100
C. $1,000
D. $16,462
E. None of the above

How much stock does the farmer need to purchase?
A. $16,824
B. $51,100
C. $1,000
D. $16,462
E. None of the above

How much stock is returned to the farmer when the loan is retired?
A. $16,824
B. $51,100
C. $1,000
D. $16,462
E. None of the above

What is the annual loan payment?
A. $16,824
B. $51,100
C. $1,000
D. $16,462
E. None of the above


What is the actuarial rate?
A. 12%
B. 12.44%
C. 3%
D. 4%
E. None of the above


What is the APR?
A. 12%
B. 12.44%
C. 3%
D. 4%
E. None of the above

What is the effective rate?
A. 12%
B. 12.44%
C. 3%
D. 4%
E. None of the above

Explanation / Answer

Question 1: The borrower needs to cover loan amount (50000), fee of ($100) and a stock of 1000.

So total money needed = 50,000 + 1000 + 100 = 51,000 Answer (Option B)

Question 2: How much stock purchase is needed to be done?

Since 2% of 50000 =1000 and since both are same, the farmer needs to purchase stock of $1,000

Answer : $1000(Option C)

Question 3: How much of the loan is returned?

Answer: None of the above(Option E)

Since the stock purchased is set off against the last loan instalment repayment, nothing is returned to the farmer

Question 4: How much is the annual loan payment?

The annual loan installments are given by "PMT" formula in excel as in =pmt(rate,nper,pv) where rate = 12% =0.12, nper = 4 and pv = 50000.

Hence the annual loan payment = pmt(0.12,4,50000) = $16,462

Hence answer is : 16,462 (Option D)

Note: We have answered 4 sub parts of the question. Kindly repost the remaining subparts for experts to answer.

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