Question

Bank A pays 5% simple interest on its deposit account, whereas Bank B pays interest on its deposit account compounded monthly.
Formulate the quoted and effective interest rates that Bank B should set if it wants to match Bank A, assuming a 6-years horizon period

Answer 1

For bank A, amount of $1 after 6 years
= 1 + (1)(.05)(6)
= 1.30

for bank B, let the monthly rate be i
amount of $1 after 6 years
= 1(1+i)^72

so (1+i)^72 = 1.3
take the 72 nd root of both sides
1+i = 1.3^(1/72) = 1.00365..
i = .00365
annual rate compounded monthly = .0438 or 4.83%