Question

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

• Initial loan amount is $52,000.
• The loan will be fully amortized in 3 years at 10%.
• Marginal tax rate is 15%.

(i) What is the tax saving in the 1^st year?

a. $917.65                  b. $780.00     

c. $663.00                   d. None of the answers are correct   

(ii) What is the tax saving in the 2^nd year?

a. $626.00                  b. $640.41     

c. $462.70                   d. $544.35

(iii) What is the total interest payment for this loan?

a. $9,405.56               b. $12,287.97

c. $10,729.91             d. None of the answers are correct

Answer 1

Initial Loan Amount =$52000

Period 3 years

Rate 10%

Annual Payment will be given by, Initial loan = Annual Payment *(1-(1+r)^-n)/r

or, 52000= A*(1-(1+10%)^-3)/10%

or, 52000= A*(1-(1.1)^-3)/.1

or, 52000= A*(1-0.75)/.1

or, 52000= A*0.25/.1

or, A= 52000*0.1/0.25

or, A= $20909.97

Interest in first year- 10%*52000=$5200

Interest of $5200 will reduce the profit by same amount hence saving of tax = tax rate* interest amount

i) Hence tax saving = 15%*5200 = 15/100*5200 = $780 i.e option b

ii) Principal paid in year 1 = 20909.97 - 5200 = $15709.97

Hence Principal Due in year 2 beginning = 52000-15709.97 = $36290.03

Hence Interest payment in year 2 = 10%*36290.03 = $3629

Hence tax saving = 15%*3629 = $544.35 i.e option d

iii) Principal paid in year 2 = 20909.97 - 3629 = $17280.97

Hence Principal Due in year 3 beginning = 36290.03-17280.97 = $19009.06

Hence Interest payment in year 3 = 10%*19009.06 = $1900.9

Hence total interest = 5200+3629+1900.9 = $10729.9 i.e option c