Question

1. The bank offers a certificate of deposit (CD) with a stated interest rate of 8.00% per year, compounded semi-annualy. While another bank offers a CD with an interest rate of7.92% per year, compounded monthly. Which CD should you invest in if you want to maximize your effective annual rate (EAR)?

2. An insurance company is offering a product called "retirement insurance." the retirement insurance promises to pay you 20,000 per year, with the first payment coming a year after your 85th birthday. The annual payments will last forever. You plan to buy this insurance on the day of your 35th birthday. If the relevant interest rate is 4% per year, what lump sum will you pay for the retirement insurance?

Answer 1

1

EAR = [(1 +stated rate/no. of compounding periods) ^no. of compounding periods - 1]* 100

? = ((1+8/(2*100))^2-1)*100

Effective Annual Rate% = 8.16

EAR = [(1 +stated rate/no. of compounding periods) ^no. of compounding periods - 1]* 100

? = ((1+7.92/(12*100))^12-1)*100

Effective Annual Rate% = 8.21

Choose 7.92 @ 12 month compounding

2

PV of perptual cF = perpetual CF/interest =20000/0.04=500000

Future value = present value*(1+ rate)^time

500000 = Present value*(1+0.04)^50

Present value = 70356.31