# Thread: SIMPLE continuous compound interest problem?

1. ## SIMPLE continuous compound interest problem?

Brandy is planning on investing 5000 and is considering two savings accounts. The 1st account is continously compounded and offers a 3% interest rate. The 2nd is annually compounded and offers a 3% interest rate, but the bank will match 4% of the initial investment. How many years will it take for the continuously compounded account to catch up with the annually compounded savings account?

I already have an equation for both accounts, but I don't understand how to solve this problem or what it means for the bank to match 4% of the initial investment.

2. ## Re: SIMPLE continuous compound interest problem?

Hey hunnyelle.

I'm not 100% sure without knowing the book you use or its conventions, but typically when you match something financially, it means you provide that specific amount.

Now if this is in addition to the interest already generated (and I am making the assumption that it is), then it means that whenever the matched portion is added, you simply add 0.04*A(0) where A(0) is the value (in dollars) of the asset at time t = 0 at the time whenever it is matched.

If it is matched initially then you simply have a formula for the interest of the non-compounded asset model (call it A(t)) and you create a new asset model A*(t) where A*(t) = A(t) + 0.04*A(0). If it's added at another time, then you add it at that time.

I'm thinking that it will be added initially as soon as you initiate the lending agreement so in this case you will compare A*(t) to your other asset model instead of comparing A(t) to the other asset model directly.