Luke invests $4200 in an account that has an annual interest rate of 2.8% compounded semi-annually. Todd invests $3900 into an account that has an annual interest rate of 3.3% and is compounded continuously. After 8 years what is the difference between the two accounts?

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