Question

Suppose ABC Bank offers to lend you $1,000 at a nominal rate of 8%, compounded monthly. The loan (principal plus interest) must be repaid at the end of the year. Bank XYZ also offers to lend you the $1,000, but it will charge 9%, with interest due at the end of the year. What is the difference in the effective annual rates charged by the two banks?

Answer 1

Answer:

The difference in the effective annual rates charged by the two banks is:

0.7%.

Explanation:

a) Data and Calculations:

ABC Bank lending = $1,000

Rate of interest = 8% compounded monthly

Effective monthly rate of interest = 8%/12 = 0.667

FV (Future Value) $1,083.00

PV (Present Value) $1,000.00

N (Number of Periods) 12.000

I/Y (Interest Rate) 0.667%

PMT (Periodic Payment) $0.00

Starting Investment $1,000.00

Total Principal $1,000.00

Total Interest $83.00

Effective annual interest rate = $83/$1,000 * 100 = 8.3%

Bank XYZ lending = $1,000

Rate of interest = 9% annually

FV (Future Value) $1,090.00

PV (Present Value) $1,000.00

N (Number of Periods) 1.000

I/Y (Interest Rate) 9.000%

PMT (Periodic Payment) $0.00

Starting Investment $1,000.00

Total Principal $1,000.00

Total Interest $90.00

Effective annual interest = 9%

Difference in rates = 9% - 8.3% = 0.7%

b) Bank XYZ charges more interest by 0.7% thank ABC Bank.