# Continous Interest

1. Jul 29, 2008

### Tiburon11`

I was reviewing continous interest formulas when something stumped me.

The accepted formula for continous interest is A=Pert, and the proof of it is simple enough to understand.

However, my math book solves the formula in a different way. It starts with the standard model for growth rate, P=P0ekt, and than solves for k.

Example: Determine how much money will exist in an account if Ed deposits 1000\$ in an account with 5% interest for 5 years.

Case 1:
A=Pert
A=1000e(.05)(5)

Case 2:
P=P0ekt
P=1000ekt

Evaluate the amount at one year to solve for k.

1000(1.05)=1050
1050=1000ek(1)

Solve for k.

1050/1000=ek(1)
k=ln(1.05)
P=1000eln(1.05)t

The growth constants are different in both cases. What is the cause of this?

2. Jul 29, 2008

### Redbelly98

Staff Emeritus
In Case 1, you are letting 5%-per-year be the growth constant (the "r" in the exponent).
This gives an annual yield (different than the growth rate) of
e^0.05 - 1
= 1.05127... -1
= 0.05127... or 5.127...%

In Case 2, you are saying the the annual yield (not the growth rate) is 5%.

The 5% represents a different parameter in the two cases: it's the growth constant in Case 1, and it's the annual yield in Case 2.