Question

A company that needs to borrow $1000000 is offered different terms from 2 banks. Bank A expects the load to be amortized with annual payments at an annual interest rate of i=.08. Bank B requires annual interest payments at a rate of i=.06 and annual deposits into a sinking fund that earns interest at i=.02. In both cases the loan is to be paid off in 10 years.

Which bank is offering the better deal? Calculate the total annual cost of each bank's loan

Answer 1

Bank A

Annual interest rate i = 0.08

Tenure n = 10 years

Initial loan amount P = $1,000,000

Total amount paid

F = P(1+i)^n

= $1,000,000 x (1.08)^10

= $2,158,925

Bank B

Annual interest rate i = 0.06

Tenure n = 10 years

Initial loan amount P = $1,000,000

Sinking fund interest rate = 0.02

Total amount paid

F = P(1+i)^n + P*i/[(1+i)ⁿ - 1]

= $1,000,000 x (1.06)^10 + $1,000,000*0.02/[(1.02)¹⁰ - 1]

= $1,790,848 + $91,327

= $1,882,175

Bank B is offering the better deal