Bank America offers 1% interest every month. Bank Boston has a clever marketing department and advertises 12% interest every year! Is this the same deal? If not, which is better? Show your thinking.

Answer 1

Despite the fact that the overall interest for the year is 12% in both cases, interest compounded monthly will yield a slightly higher result than interest compounded annually.

The general form for the compound interest equation is:

where A(t) is the amount of money your bank account is worth after any time "t" (with "t" measured in years), A₀ is the initial amount deposited, "r" is the annual interest rate, "n" is the number of compounding periods per year, and, again, "t" is the time gone by in years.

For the purposes of illustration, let's assume we put in $1000 into an account in both banks:

So for Bank America, 1% interest per month, r = 12% = 0.12, n = 12, t = 1. so:

The amount the account is worth after 1 year is A(1) = 1000(1 + 0.12/12)¹²⁽¹⁾ = 1000(1.01)¹² = $1126.83

And for Bank Boston, 12% interest per year, r = 12% = 0.12, n = 1, t = 1. so:

The amount the account is worth after 1 year is A(1) = 1000(1 + 0.12/1)¹ = 1000(1.12)¹ = $1120.00

So you get an extra $6.83 with Bank America after 1 year