Question

1.	You have invested $48,000 in a security that will earn a continuously compounded rate of 12% for a period of 15 years. What amount will the investment grow to by the end of the investment?

2.	Your bank is offering you an investment that will return $50,000 in exactly 16 years. The discount rate is 5% per year with continuous compounding/discounting. What is the most you should pay for this investment?

3.	A bank offers you a credit card with a stated APR of 8%. Upon closer inspection you see that the loan continuously compounds. What is the EAR on this continuous compounding loan?

4.	Joe’s Pizza, Inc. just paid a dividend, D0, of $1/share on its common stock. Investors expect that its dividend will grow at a constant rate of 10% per year, and they require a return of 15% on this stock. What is the value of this stock based on the discounted dividend model?

5.

Mike’s Pizza just paid a dividend, D0, of $0.50/share on its common stock. Investors expect that its dividend will decline at a constant rate of 10% per year. That is, the expected growth rate g is -10%. They require a return of 15% on this stock. What is the value of this stock based on the discounted dividend model?

Answer 1

First 2 questions are being answered here:

1. Here, we will use the following formula of continuous compounding:

FV = PV * e(i*t)

where, FV is the future value, PV = Present value = $48000, i = rate of interest = 12%, t is the time period = 15 and e is the exponential factor whose value is 2.7183

Putting the values in the above formula, we get,

FV = $48000 * (2.7183)15 * 12%

FV = $48000 * (2.7183)1.8

FV = $48000 * 6.04972025932

FV = $290386.57

So, investment will gros to $290386.57

2. Here, we will use the following formula of continuous compounding:

FV = PV * e(i*t)

where, FV is the future value = $50000, PV = Present value, i = rate of interest = 5%, t is the time period = 16 and e is the exponential factor whose value is 2.7183

Putting the values in the above formula, we get,

$50000 = PV * (2.7183)16 * 5%

$50000 = PV * (2.7183)0.8

$50000 = PV * 2.22555283056

PV = $50000 / 2.22555283056

PV = $22466.33

So, we should pay $22466.33 for this investment.