This problem has to do with exponential models. The question says, you deposit $1600 in a bank account. Find the balance after 3 years for each of the following situations. The first one says:

Question

1. The account pays 2.5% annual interest compounded monthly.
2. The account pays 1.75% annual interest compounded yearly.
3. The account pays 4% annual interest compounded yearly.
For the first one, I think that I'm supposed to solve the equation this way: $1600 (1+.025/12 which is 1.0028)^36, since it's three years. I tried doing this same formula for the other two, except changing monthly to quarterly and yearly, but it doesn't work out. The other two are smaller numbers than the first, which doesn't make sense because it should increase. Can someone please help me?

Answer 1

Your first number should have been
1600*(1.00208333)^36 = $1724.48
You left out a 0 after the 2 in the 1.0020833, and you should not have rounded off to five significant figures. You need a total of at least six significant figures to keep track of the principal accurately.

Your third number should be
1600(1.04)^3 = $1799.78, which is not less than the first.

The second case of course returns less because of the very low 1.75% interest rate.

Answer 2

Thank you.