Part I: Solve 4 of the following time value of money problems by filling in the
ID: 2425124 • Letter: P
Question
Part I:
Solve 4 of the following time value of money problems by filling in the 4 columns to the right of the description.
Be sure to solve 1 problem from each of the following 4 categories listed under Problem Types. I have completed the first row as an example.
Part II:
Discuss how you may use time value of money concepts in your personal life. For example, saving for college tuition or retirement, paying off a car loan or home mortgage. Give specific details as to how you would use these formulas for more effective decision making. Create 1 description and fill in the table for your newly created question.
Problem Types:
1 pv = present value of $1
2 fv = future value of $1
3 PVAo = Present Value of an Ordinary Annuity of $1 (payment at end of period)
4 FVAo = Future Value of an Annuity of $1 (payment at end of period)
Description Type of Problem Table Formula Answer 1 How much money must your rich uncle give you now to finance four years of college, assuming an annual cost of $48,000 and an interest rate of 6% (applied to the principal until disbursed)? Present Value of an ordinary Annuity PVAo PV = 48,000 (3.465) $166,325.07 2 How much interest would you earn if you deposited $300 at 6 percent for 27 months? 3 If you deposit $2,000 in a 5-year certificate of deposit at 5.2%, how much will it be worth in five years? 4 How much interest would you pay to borrow $670 for eight months at 12 percent? 5 You wish to borrow $18,000 to buy a new auto-mobile. Rate is 8.6% over five years with monthly payments. Find the monthly payment. 6 What is the future value of $800 at 8 percent after six years? 7 How much would you have in savings if you kept $200 on deposit for eight years at 8% compounded semiannually? 8 You choose to invest $50/month in a 401(k) that invests in an international stock mutual fund. Assuming an annual rate of return of 9%, how much will this fund worth if retiring in forty years? 9 What is the future value of an annual deposit of $230 earning 6 percent for 15 years? 10 If you invest $600/Year in a 401(k) that invests in an international stock mutual fund. Assuming an annual rate of return of 9%, how much will this fund worth if retiring in forty years? 11 What amount would you have in a retirement account if you made annual deposits of $375 for 25 years earning 12 percent, compounded annually? 12 What is the present value of $2,200 earning 15 percent for eight years? 13 How much money must you set aside at age 20 to accumulate retirement funds of $100,000 at age 65, assuming a rate of interest of 7%? 14 To have $6,000 for a child’s education in 10 years, what amount should a parent deposit in a savings account that earns 12 percent, compounded quarterly? 15 If you deposit $2,000 in a 5-year certificate of deposit at 5.2% with quarterly compounding, how much will it be worth in five years? 16 What is the present value of a withdrawal of $200 at the end of each year for 14 years with an interest rate of 7 percent? 17 How much would you have to deposit now to be able to withdraw $650 at the end of each year for 20 years from an account that earns 11 percent? 18 What would be the annual payment amount for a $20,000, 10-year loan at 7 percent?
Explanation / Answer
Type of problem Table Formula Answer How much interest would you earn if you deposited $300 at 6 percent for 27 months? FV=Future value of $1 FV at $1 table FV=300*factor fv at 13.5% 40.5 Note How much interest would you pay to borrow $670 for eight months at 12 percent? FV=Future value of $1 FV at $1 table FV=PV*factorFv=670*1.08=$723.6 Interest=723.6-670 =53.6 53.6 Note 6% for 1 year so for 27 months rate is 13.5% and for one year calculation FV 342 300*1.14 FV at 14% 339 300*1.13 FV at 13% So interest is between 342 FV at 14% 339 FV at 13% S0 interest is= 339-300(-(342-339)/2) as interes is 13.5% So for .5% that is half of du=ifference between 342-339=1.5 and add 339-300=39 Total interst=39+1.5 40.5
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