Beatrice invests €1,000 in an account that pays 4% simple interest.How much more could she have earned over a ﬁve-year period if the interest had compounded annually?

Question

Quizplus · Accepted Answer

Using the formula for simple interest, Beatrice would earn:

Year 1: €40
Year 2: €40
Year 3: €40
Year 4: €40
Year 5: €40
Total: €200

To calculate the amount earned with annually compounded interest, we use the formula:

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

Where:
A = the amount of money at the end of the time period
P = the principal (initial amount invested)
r = the annual interest rate (as a decimal)
n = the number of times the interest is compounded per year
t = the time (in years)

Plugging in the values, we get:

A = €1,000(1 + 0.04/1)^(1*5)
A = €1,216.65

So, the difference between the two amounts is:

€1,216.65 - €1,000 = €216.65

Therefore, Beatrice could have earned €216.65 - €200 = €16.65 more with annually compounded interest. The correct answer is C.

Beatrice Invests €1,000 in an Account That Pays 4% Simple