Question

1）You are planning for your retirement in 30 years. At that time you want to have saved $8,500,000. How much do you need to save each month for the next 30 years if the interest rate on your investment will be 7% per year (APR)?

2）Suppose a condo generates $28,000 in cash flow at the end of the first year. If the cash flows grow at 5% per year, the interest rate is 12%, and the building lasts forever, what is the most you would be willing to pay for the condo?

3）An online marathon fund raiser continues as long as donations keep coming in. The first hour costs $1.00, and then the cost per hour goes up by 3% every hour. Suppose the fundraiser lasts for 129 hours.

How much will be raised in the last hour? Enter your answer rounded to two decimal places.

How much will be raised in total? Enter your answer rounded to two decimal places.

Answer 1

1) FV of Retirement fund =8500000
Rate per month =7%/12
Number of Months =30*12 =360
Amount to be saved per month=FV/((1+r)^n-1)/r) =8500000/((1+7%/12)^360-1)/(7%/12))=6967.38

2) The most you will be bidding for the condo =Cash Flow in Year 1/(Required Rate-Growth) =28000/(12%-5%)=400000

3) First cost =1
Growth rate =3%
Rate(r)=(1+3%) =1.03
Amount raised in last hour =First cost*(1+r)^(n-1) =1*(1+3%)^(129-1) =43.97
Total amount raised =1*((r^n-1)/(r-1)) =1*((1.03^129-1)/0.03) =1476.33