1. You have a child that is 10 years old, and would like to start saving up for
ID: 2638842 • Letter: 1
Question
1. You have a child that is 10 years old, and would like to start saving up for their college education. You would like be able to pay $35,000 each year for four years of college starting 8 years from now (in years 8-11). How much do you need to save annually in years 1-7 to meet your goal, if you can earn a real annual return of 11% on your college savings account?
2. You are offered $1000 (in nominal dollars) 6 years from now in exchange for a loan of $750 today. You expect inflation to run 3.3% per year, and your real hurdle rate is 5%. Should you make the loan?
3. You would like to have $10000 (in real $) in an account 80 years from now. If the annual inflation rate is expected to be 2.2%, and you expect a nominal annual return of 5.5% on the account, how much would you need to put in today?
4. You buy a car, and take out a loan for $18,000 that has equal nominal annual payments over the next five years. The real rate of return on the loan is 3.9%, and the annual inflation rate is 2%. What will the payments be?
5. You have $1000 in an account that yields a nominal return of 5%. If the inflation rate is 2%, how long will you have to leave your money in the account for it to double in real terms?
6. A project costs $2000 immediately. The project yields nominal returns of $100 in year 1, $200 in year 2, $300 in year 3, $400 in year 4, and $500 in year 5. In addition, the project will have capital worth $1000 (in nominal $) left over in year 5. The real discount rate is 5% and the expected inflation rate is 2%. What is the NPV of this project?
7. You have $1000 to invest, and are choosing between two projects, both of which cost $1000 up front and will yield six years of returns. The returns for the first investment will start at $200 (in nominal $) a year from now and increasing at 8% annually. The returns for the second start at $250 (in real $) and increase at 2% annually. If your real hurdle rate is 3% and the expected inflation rate is 2.2%, which of these investments should you choose (if any)?
CAN YOU EXPLAIN ?
Explanation / Answer
1> PV of the fund required at Y8=PV(A=35000,N=4,I=11%)=3.1024*35000 108584 Compound Value of Annuity from Y1-Y7 108584 Interest Factor=F=1.11^7 2.076 A*(F-1)/F=A*(2.076-1)/0.11=9.78A 108584 or A=108584/9.78 11102.66 2> Interest Rate=Hurdle Rate+Inflation=5+3.3 8.3 FV=750*(1.083^6) 1210.13 Since 1000 Interest Rate=5.5+2.2 7.7 A*(1.077^80)=10000 or 377.79A=10000 or A=10000/377.79 26.47 4> Interest Rate=3.9+2 5.9 Intrest Factor=F=(1.059^5) 1.33 Capital Recovery=A=P*F*i/(F-1)=18000*1.33*0.059/(1.33-1) 4280.18 5> Real interest=5-2 3 Doubling Period=0.35+(69/3) 23.35 6> Nominal Discount=5+2 7 NPV=-2000+100/(1.07)+200/(1.07^2)+300/(1.07^3)+400/(1.07^4)+500/(1.07^5)+1000/(1.07^5) -112.328 7> Discount Rate=3+2.2 5.2 Project-1 : ((1+g)/(1+r))^n=(1.08/1.052)^6 1.17 Project-2 : ((1+g)/(1+r))^n=(1.02/1.052)^6 0.83 PV of growing annuity of Project A=(200/(0.052-0.08))*(1-1.17) 1214.29 PV of growing annuity of Project B=(250/(0.052-0.02))*(1-0.83) 1328.13 Project B gives better inflow and should be selected.Related Questions
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