Question

.A risk-free investment promises to pay you $550 every 6 months for the next 11 years. If you can earn 9.5% on your money, how much would you be willing to pay for this investment?

You want to retire and have annual payments of $50,000 over a 20 year period. You plan to retire in 17 years. If you can earn 7.5% on your funds, how much do you need to invest monthly until you retire to reach your goal?

You have a choice of $1 million in 50 years or $2,000 today. If your interest rate is 14%, which would you choose? (show your work to receive credit).

Answer 1

1.
=Amount/(rate/2)*(1-1/(1+rate/2)^(2*n))
=550/(9.5%/2)*(1-1/(1+9.5%/2)^(2*11))=7407.56132425818

2.
Assuming 7.5% is compounded monthly
rate compounded annually=(1+rate/12)^12-1=(1+7.5%/12)^12-1=7.763%

Present value in 17 years of retirement payments=amount/rate*(1-1/(1+rate)^n)=50000/7.763%*(1-1/(1+7.763%)^20)=499687.6254

Monthly investments=Future value*(rate/12)/((1+rate/12)^(12*n)-1)=499687.6254*(7.5%/12)/((1+7.5%/12)^(12*17)-1)=1217.785681

3.
Present value of 1 million=Future value/(1+rate)^t=1000000/1.14^50=1428.09610012869

Choose 2000 today as it has higher present value