Answer:
1) Suppose you were to save $500.0000 in the first bank. The interest rate is r1=8.0000%. Three years from now, you should have
effective interest rate = 1.08 = (1 + r)¹²
r = 0.643403% per month
future value = $500,000 x (1.0643403)³⁶ = $629,856
2) Suppose you were to save $500.0000 in the second bank. The interest rate is r2=5.0000%. Three years from now, you should have
effective interest rate = 1.05 = (1 + r)³⁶⁵
r = 0.013368061% per day
future value = $500,000 x (1.00013368061)¹⁰⁹⁵ = $578,812.50
3) Suppose you were to save $500.0000 in the third bank. The interest rate is r3=3.0000%. Three years from now, you should have
future value = $500,000 x e⁰°⁰⁹ = $547,087.14
4) Let the interest rate in the first bank be r1=8.0000%, and you are considering saving your money for 3 years. The interest rate from the second bank that would make you indifferent between the first and second bank is r2=
$629,856 = $500,000 x (1 + i)¹⁰⁹⁵
(1 + i)¹⁰⁹⁵ = 1.259712
1 + i = 1.000210874
i = 0.000210874 = 0.0210874% per day or 7.7% annual
5) Let the interest rate in the third bank be r3=3.0000%, and you are considering saving your money for 3 years. The interest rate from the first bank that would make you indifferent between the first and third bank is
$500,000 x (1 + i)³⁶ = $547,087.14
(1 + i)³⁶ = 1.09417428
i = 0.2503128 per month = 3.05% annual
