Question

You purchase a three year certificate of deposit (CD) for $100,000 on January 1st, 2000. This CD has an annual interest rate of 5%. The interest compounds continuously. What is the balance for the CD account on July 1, 2001?

$105,000

$107,500

$107,593

$110,250

Answer 1

Answer: Formula of Continuous compounding-

FV = PV * ert

Where:

• FV = Future value,
• PV = Present Value.
• e = exponential factor
• r= Rate of interest
• t = time

Given: PV = $100000, e = 2.7183 (constant), r = 5%, t = 1. 5 years (From Jan 1, 2000 to July 2001)

Putting the values in the formula we get:

Firstly we will calculate the Future value at the end of Year 1. So t = 1

FV = 100000 * 2.7183(.05*1)

FV = $107593

Now, we will calculate FV 1.5 years, i.e. 1 year 6 months

FV = 100000 * 2.7183 (.05*1.5)

FV = $107788