Question

Arnold wants to borrow $800000 for 7 years. Bank A will lend the money at j₁ = 9%, if it is amortized by quarterly payments. Bank B will lend the money at j₁ = 6% if only the interest is paid quarterly and the principal is paid in a lump sum at the end of 7 years. If Arnold chooses bank B he will develop a sinking fund making quarterly payments earning j₁₂ = 6%. How much will Arnold save per payment by choosing the better option? *please do not round intermediate steps*

Answer 1

Arnold has two options (Bank A & Bank B)

1. Payment of quarterly installments (Bank A)

Loan amount = $800,000

Life = 7 years

Interest = 9%

We cab calculate the instalment amount using Present value of annuity factor (PVAF) at 2.25% (9%/4) for 28 periods (7 x 4)

Instalment amount = Loan amount/PVAF

= $800,000/20.6078

= $38,820.2525

2. Quarterly Interest payment and Lumpsum principal along with sinking fund creation (Bank B)

Quarterly interest payment = 800,000 x 6% x 3/12

= $12,000

Sinking fund is created when there is future fixed cash Outflow. Under this we will make deposit to this fund periodically and invest the funds to mature at certain future point to meet future obligations.

Sinking fund quarterly amount ( future value of annuity at 1.5% (6%/4) & for 28 periods (7x4))

= Future Cashoutflow/ Future value of annuity at 1.5% for 28 periods

= 800,000/34.4814787

= $23,200.8612

Total quarterly Outflow = $23,200.8612 + $12,000

= $35,200.8612

Arnold will choose Bank B, he will save $3,619.3913 ($38,820.2525-$35,200.8612) per payment by choosing this option