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
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
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