Question

show how to solve the next 3 problems(show work)

1. You are starting your four-year college education today, and you are worried if you have enough money in your account for tuition and fees. You are going to pay $15,000 a year at the beginning of each school year starting today. If the interest rate on your account is 7%, compounded annually, how much should you have in your account today? Round to the nearest cent.

2. How much would an investor be willing to pay for an investment which promises to pay $200 per year in perpetuity if the investor requires a 14 percent return on the investment? Round to the nearest cent.

3. If you are going to receive $70,000 for 20 years starting 5 years from now, what is the present value of the cash flows discounted at 12%? Round to the nearest cent. (2 decimal)

Answer 1

1. At the beginning of each year, student pays 15,000 and rate of interest is 7% annually

i.e. At the beginning of year 1 = 15,000

Therefore present value =15000

At the beginning of Year 2 = 15000

Present value = 15000/(1+r%)

= 15000/1.07 = 14018.69

At the beginning of year 3 =15000

Present value = 15000/(1+r%)^2

= 15000/(1.07^2) = 13101.58

At the beginning of year 4 = 15000

Present value = 15000/(1+r%)^3

= 15000/(1.07^3) = 12244.47

Therefore, the student should have total of 15000+14018.69+13101.58+12244.47

=54364.74

2.The investment pays 200 for perpetuity at interest rate 14%

The formula for perpetuity is Present value = Payment/ Interest rate

= 200/0.14=1428.57

3.The cash flow is 70000 from end of year 5 to end of year 25. This is annuity

Present value of cash flows at end of year 5 is

PV at the end of 5 year = (Payment /interest rate)(1-(1+interest rate)^(-n))

= (70000/0.12)(1-1.12)^(-20)=522861.05

Discounting it to present value = 522861.05/(1.12)^5= 296685.40