# Interest Rate problem: An initial deposit of $2800 is made #### Goods ##### New member An initial deposit of$2800 is made in a savings account for which the interest is compounded continuously. The balance will triple in eight years. What is the annual rate of interest for this account?

Do I use the simple interest equation: I=Prt?!!

Thank you!!

#### skeeter

##### Senior Member
for continuously compounded interest ...

$$\displaystyle \L A = A_0 e^{rt}$$

where A = account balance at any time t in years
A<sub>0</sub> = initial account balance at t = 0
e = base of the natural log, approx 2.718281828459045...
r = interest rate per year as a decimal
t = time in years

for your problem, substitute in the known values ...

$$\displaystyle \L 3A_0 = A_0 e^{r*8}$$

$$\displaystyle \L 3 = e^{r*8}$$

$$\displaystyle \L ln(3) = r*8$$

$$\displaystyle \L \frac{ln(3)}{8} = r$$

r = approx 13.7 % APR

#### tkhunny

##### Moderator
Staff member
Re: Interest Rate problem

Goods said:
..."the interest is compounded continuously."
"Do I use the simple interest equation: I=Prt?!!"
No.

#### Denis

##### Senior Member
Interest compounds continuously:
e^(8r) = 3
r = .1373265360835...

Interest compounds every second on a 365 days basis (p = 365*24*60*60):
(1 + r/p)^(8p) = 3
r = .1373265363798...

Put 'em together for a "look":
13.7326536 0835...%
13.7326536 3798...%

Ahem