Finite math

Question

How long will it take for $5700 to grow two 34,800 and interest-rate of 3.8% but the interest is compounded continuously

Answer 1

Hello, thank you for taking the time to post your question!

The underlying formula that you want to use here for interest compounded continuously is

A = P e^(rt)

For the information from this question that becomes

34,800 = 5,700 * e^(0.038t)

If you solve that algebraically for the value of t it should be

t = 47.61 years, meaning that it would take about 48 years for the amount to grow from $5,700 to $34,800 at this interest rate

I hope that helps get you moving in the right direction! Feel free to reach out if you have any additional questions beyond that :)

Answer 2

For continuous compounding, the formula is:

 

A = Pe^rt

 

Where A = Final amount of money, P = initial investment (principle), r = annual interest rate (expressed as a decimal value), t= time in years.  To solve for t:

 

ln(A) = ln(Pe^rt) = ln(P) + ln(e^rt) = ln(P) + rt

 

ln(A) - ln(P) = rt

 

ln(A/P)/r = t

 

Plug in the values (remember r = 0.038) and solve for t.