Answer:
Step-by-step explanation:
Considering Luke's investment,
Initial amount invested is $4200 This means that the principal is
P = 4200
It was compounded semi annually. This means that it was compounded twice in a year. So
n = 2
The rate at which the principal was compounded is 2.8%. So
r = 2.8/100 = 0.028
The investment was made for 8 years. So
t = 8
The formula for compound interest is
A = P(1+r/n)^nt
A = total amount in the account at the end of t years. Therefore
A = 4200 (1+0.028/2)^2 × 8
A = 4200(1.014)^16 = $5246.34
Considering Todd's investment,
The formula for continuously compounded interest is
A = P x e (r x t)
where e is the mathematical constant approximated as 2.7183
Therefore
A = 3900 × 2.7183^(0.033 × 8)
A = 3900 × 2.7183^(0.264)
A = $5078.3
The difference between the two accounts after 8 years would be
5246.34 - 5078.3 = $168.04
