11 December, 17:36

# 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?

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1. 11 December, 18:09
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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