Question

A farmer is considering borrowing money from a bank. Given the following information:

• Initial loan amount is $250,000.
• The loan will be fully amortized in 3 years at 14%.
• Marginal tax rate is 15%.

(i) What is the loan balance at the end of 1^st year?

a. $195,791.34          b. $177,317.13          

c. $253,676.47           d. None of the answers are correct           

(ii) What is the loan balance at the end of 2^nd year?

a. $129,880.74           b. $117,789.86          

c. $94,458.66             d. None of the answers are correct

Answer 1

Annual Loan Payment

Loan Amount (P) = $250,000

Interest Rate (n) = 14% per year

Number of years (n) = 3 Years  

Annual Loan Payment = [P x {r (1+r)ⁿ} ] / [( 1+r)ⁿ – 1]

= [$250,000 x {0.14 x (1 + 0.14)³}] / [(1 + 0.14)³ – 1]

= [$250,000 x {0.14 x 1.48154}] / [1.48154 – 1]

= [$250,000 x 0.207416] / 0.48154

= $51,854.04 / 0.48154

= $1,07,682.87 per year

Loan Amortization Schedule

Year	Beginning Amount	Payment	Interest Paid at 14%	Principal Paid	Ending Balance
1	2,50,000.00	1,07,682.87	35,000.00	72,682.87	1,77,317.13
2	1,77,317.13	1,07,682.87	24,824.40	82,858.47	94,458.66
3	94,458.66	1,07,682.87	13,224.21	94,458.66	0.00

Final Answers

The loan balance at the end of 1st year = (b). $177,317.13

The loan balance at the end of 2nd year = (c). $94,458.66