Continuous Growth of Interest

[justan4cat]

How long will it take for $8200 to grow to $45,200 at an interest rate of 10% if the interest is compounded continuously?

Can I use this formula? A=P(1+i)[sup:247ptvae]t[/sup:247ptvae] It was for "annual" growth in my book. The question states compounded continuously but I only see one formula related to interest in my book.

if so, do I plug in the numbers like this?:

45200=8200(1+.10)[sup:247ptvae]t[/sup:247ptvae] Then divide both sides by 8200

I get: 45200/8200=(1+.10)[sup:247ptvae]t[/sup:247ptvae]

But then what?

 

[Deleted member 4993]

How long will it take for $8200 to grow to $45,200 at an interest rate of 10% if the interest is compounded continuously?

Can I use this formula? A=P(1+i)[sup:2xtnbt6d]t[/sup:2xtnbt6d] It was for "annual" growth in my book. The question states compounded continuously but I only see one formula related to interest in my book.

if so, do I plug in the numbers like this?:

45200=8200(1+.10)[sup:2xtnbt6d]t[/sup:2xtnbt6d] Then divide both sides by 8200

I get: 45200/8200=(1+.10)[sup:2xtnbt6d]t[/sup:2xtnbt6d]

But then what?

For continuous compounding, the formula is:

A = P * e[sup:2xtnbt6d]rt[/sup:2xtnbt6d]

t = 1/r * ln(A/P)

 

[justan4cat]

Thanks. From there, I get:

t=1/.10* LN (45200/8200)
t=10*1.70696
t=17.1 years