Compound interest

Question

Stockman's bank will pay 4.2% compounded annually, on a saving account. A competitor, Mesalands savings, offers monthly compounding on savings accounts. What is the minimum annual interest rate that Mesalands need to pay to make it's annual yield exceed that of Stockman's?

Answer 1

Let r = the unknown rate (as a decimal).  For an initial investment of P₀ in both accounts, we want the Mesaland investment to be higher after 1 year (12 months):

 

P₀*(1 + r/12)¹² > P₀*(1.042)¹

(1 + r/12)¹² > 1.042

(1 + r/12) > (1.042)^1/12

r/12 > (1.042)^1/12 - 1

r > 12[(1.042)^1/12 - 1]

 

Use your calculator to get the answer.  Multiply r by 100% to convert to a percent.