Question

If $8500 is invested at 12.7% compounded continuously, the future value S at any time t (in years) is given by the following formula. (Round your answers to two decimal places.) S = 8500e0.127t
(a) What is the amount after 18 months? S = $

(b) How long before the investment doubles? t = yr

Answer 1

Answer:

Given formula is :

S = $8500e^{0.127t}$

We have p = 8500

r = 12.7% or 0.127

(a) when t = 18 months or $\frac{18}{12}=1.5$ years

S = $8500e^{0.127(1.5)}$

=$8500e^{0.1905}$

=$e^{0.1905}$= 1.20985

S = $10283.73

(b) Investment doubles means S = $8500\times2=17000$

$17000=8500e^{0.127t}$

$\frac{17000}{8500}=e^{0.127t}$

=> $2=e^{0.127t}$

Taking log on both sides

$ln(2)=ln(e^{0.127t})$

We get t = 5.45 years