Suppose you just won $10,000 in the lottery. You decide to put it all in a savings account.
A: Bank A offers you a 10% annual interest rate that compounds annually, while Bank B offers you a 10% annual interest rate compounded every 6months.
(a) How much will you have in the bank at the end of the year if you go with Bank A?
(b) How much will you have if you put your money into Bank B?
(c) What annual interest rate would Bank A have to offer to make you indifferent between accepting Bank B’s and Bank A’s offers over the coming year?
(d)Would the interest rate you calculated in (c) be sufficient for you to be indifferent between
Bank A and Bank B if you planned to keep your money in the savings account for 2 years?
B: Suppose you place x in a savings account and assume that the account gives an annual interest rate of r compounded n times per year.
(a) Derive the general formula for how much y you will have accumulated 1 year from now in terms of x, n and the annual interest rate r . Check the answers you derived in (a) and (b) of part A.
(b) If x = 10,000 and r=0.1, how much will you have at the end of the year if interest compounds monthly (i.e. n = 12)?
(c) What if interest compounds weekly?
(d) If you have to choose between an annual interest rate of 10.5% compounded annually or an annual interest rate of 10% compounded weekly, which would you choose?