Compounded Continuously (use Pe^rt formula)

Question

For an investment of $5,000 compounded continuously at 9% per year (use the "Pert" formula), answer the following, rounding to the nearest cent or cent per year:

A.) what is the formula for the amount after t years?

 

B) how long will it take to reach $12,000

 

C) what is the rate of change after t=12 years

 

D) what is amount at t=12 years

 

E) using C and D what is an estimate for the amount at t=13 years

Answer 1

Amount = Principal . e^ (Rate. Time)

Amount = 5000 e ^(0.09 t)

 

Solve 12000 = 5000 e ^(0.09 t)

12/5 = 2.4 = e ^(0.09 t)

ln(2.4) = 0.09 t

t = ln(2.4)/0.09

 

rate change = e ^(0.09) per year

 

Amount at t = 12 years      = 5000 e ^ (0.09 x 12)

 

Amount at t = 13 years       = [Amount at t = 12 years] x e ^ 0.09