1 John invested 6000 at an interest rate of 8 annually a Fin

(1) John invested $6000 at an interest rate of 8% annually. (a) Find the amount of the investment at the end of 5 years when compounded (i) quarterly (ii) Continuously (b) Determine when the amount will be tripled if compounded continuously

Solution

1. a. A=P(1+ (r/n))^nt

i) In quarterly, n=4

A=6000(1+.08/4)^4*5

=6000(1.02)²⁰=$8916

ii) A= P e^rt= 6000 e^.08*5= 6000 e^.4=$8951

b. Triple means amount becomes 3*6000=18000

Using the formula, used in part (ii)

18000=6000 e^.08*t

3=e^.08t

ln 3=.08t

t=(ln 3)/.08=13.7years