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# Compute some properties of compound interest rates

Consider a bank account which starts with dollars and pays an interest rate per year, compounding times per year.

1. Prove that the balance in the bank account at the end of years is For fixed values of and , the balance at the end of years as is given by We say that money grows at the annual rate with continuous compounding if the amount of money after years is denoted by is given by Give an approximate length of time for the money in a bank account to double if and compounds:

1. continuously;
2. four times per year.

Incomplete. Sorry, I’ll try to get back to this soon(ish).

### One comment

1. Tyler says:

I’ll give this a shot:

(a): There isn’t really much to prove, is there? This is just the formula for compound interest.

(b): Solve for t: 2P = Pe^(rt), ln(2) = rt, r = 0.06, so t = ln(2)/0.06.

(c): Solve for n: 2P = P*((1+0.06/4)^(4n)), 2 = ((1+0.06/4)^(4n)), log base 1.015 (2) = 4n,

(log base 1.015 (2))/4 = n.