A bank compounds interest continuously. What nominal interest rate does it offer if $1,500 grows to $2,500 in 10 years? Round to two decimal places.
A) 5.00%
B) 5.07%
C) 5.11%
D) 5.13%

Question

Quizplus · Accepted Answer

The formula for continuous compounding is A = Pe^(rt), where A is the final amount, P is the principal, e is the base of the natural logarithm, r is the annual interest rate, and t is the time in years.Substituting the given values into the formula, we get 2500 = 1500e^(r*10).Dividing both sides by 1500, we get e^(r*10) = 2500/1500 = 1.6666666666666667.Taking the natural logarithm of both sides, we get r*10 = ln(1.6666666666666667) = 0.5069352379227937.Dividing both sides by 10, we get r = 0.05069352379227937.Rounding to two decimal places, we get r = 5.07%.

A Bank Compounds Interest Continuously