Question

A firm will have to pay a legal settlement of $1,500,000 in 2 years. What is the present value of this obligation today if the firm can earn 6% APR compounded annually on their deposits?

How many years will it take for a single deposit of $100 to triple in value at an effective annual rate of 5%?

Which of the following rates has the greatest effective annual return (EAR)?

Check the one rate with the highest EAR:

Group of answer choices

4% APR compounded monthly

4.2% APR compounded annually

4% APR compounded daily

What is the present value of a regular perpetuity starting with a $500 cash flow next month, growing at a rate of 3.72% APR compounded monthly, if the discount rate is 9% APR compounded monthly?

Answer 1

1)

Future value of legal settlement (FV) = $ 1,500,000

Number of years = 2

APR = 6%

PV of the obligation = FV/(1+rate)^n = 1,500,000/(1+6%)^2 = $ 1,334,994.66

2)

Single deposit today (PV) = $ 100

FV of deposit = $ 300

rate = 5%

Number of years (nper) = = 22.51 years

3)

The more number of compounding , the higher the rate. Hence 4% compounded daily> 4% compounded monthly

Among 4% compounded daily and 4.2 % compounded annually,

EAR for 4% compounded daily = (1+ 4%/365)^ 365 -1 = 4.08%

Answer is 4.2% APR compounded annually

4)

Monthly amount (PMT) = $ 500

Growth rate in perpetuity (g) = 3.72%

Discount rate , k = 9%

PV of perpetuity = PMT*(1+g)/ (k-g) = 500*(1+3.72%)/(9% - 3.72%) = $ 9,821.96