You are going to loan your friend $1,000 for one year at a 5% rate of interest. How much additional interest can you earn if you compound the rate continuously rather than annually?

Question

Quizplus · Accepted Answer

We can use the formula A=Pe^(rt), where A is the final amount, P is the principal, r is the annual interest rate, e is the Euler's number (approximately 2.71828), and t is the time in years.

For annual compounding, we have A=1000(1+0.05) = $1,050 after one year.

For continuous compounding, we have A=1000e^(0.05*1) ≈ $1,051.27 after one year.

The additional interest earned is A - P - r = $1,051.27 - $1,000 - 0.05 = $1.27.

Therefore, the best choice is C.

You Are Going to Loan Your Friend $1,000 for One