If $3500 is invested at an interest rate of 8.25% per year, compounded continuously, find the value of the investment after the given number of years. (Round your answers to the nearest cent.)

Question

If $3500 is invested at an interest rate of 8.25% per year, compounded continuously, find the value of the investment after the given number of years. (Round your answers to the nearest cent.) (a) 4 years $ (b) 8 years $ (c) 12 years $

Answer 1

this is continuous growth so use the formula y= A(e^kt) where A is initial value k is growth factor (.0825) and t is time so in 4 years y=3500( e^ 4(.0825)

y= 3500(e^.33)= 4868

You can do the same calculation where t= 8 and t=12

Answer 2

Clara

8.25 % = 0.0825

So our growth factor per year is 1 + 0.0825 = 1.0825

After n years value = 3500 ( 1.0825) ⁿ

So you just need to substitute n = 4, 8, 12 here

Mike