PA 375 Lecture 15: 3/1/17
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Assume that you have $1,000 to invest, so insert 1000 as your Present Value in the following table. Assume that you want to invest your money for 5 years (insert 5 for Number of Periods). Assume an annual interest rate of 3.00% (insert 3 for Interest Rate per Period). The table will determine the Future Value of your investment. If you input the numbers correctly, your Future Value is computed to be $1.159, which is what your investment will be worth in 5 years. Now revise the input to reflect your actual savings and the prevailing interest rate so that you can see how your savings will grow in 5 years. Even if you have no savings now, you can at least see how the interest rate affects the future value of savings by revising your input in the Interest Rate per Period and then observing the change in the Future Value. Future Value of a Present Amount Present Value $1,500 Number of Periods 5 Interest Rate per Period 3.0% FV = PV*(1+R)^N Future Value $1,739 2. Assume that you have $1,000 to invest at the end of each of the next 5 years, so insert 1000 as your Payment per Period in the following table. Assume that you want to invest your money for 5 years (insert 5 for Number of Periods). Assume an annual interest rate of 3.00% (insert 3 for Interest Rate per Period). The following table will determine the Future Value of your investment. If you input the numbers correctly, your Future Value is computed to be $5,309, which is what your investments will be worth in 5 years. Now revise the input to reflect your actual expected savings per year over the next 5 years, and existing interest rate quotations so that you can estimate how your savings will grow in 5 years. You can now revise the table to fit your own desired level of saving. Future Value of an Annuity Payment per Period $1,500 Number of Periods 5 Interest Rate per Period 3.0% FV = FV(R, N, PMT, (PV), beginning=1, end=0) Future Value $7,964 3. Assume that you want to deposit savings that will be worth $10,000 in 5 years, so insert 10000 as the Future Amount and 5 as the Number of Periods in the following table. Assume an annual interest rate of 3.00% (insert 3 for Interest Rate per Period). The following table will determine the Present Value, which represents the amount of savings you need today that would accumulate to be worth $10,000 in 5 years. If you input the numbers correctly, the Present Value is estimated in the table to be $8,606. Now revise the input to reflect your own desired savings amount in 5 years so that you can estimate how much you need now to achieve your savings goal in 5 years. Present Value of a Future Amount Future Amount $20,000 Number of Periods 5 Interest Rate per Period 3.0% PV = FV / (1+R)^N Present Value $17,252 4. Assume that you want to deposit savings at the end of each of the next 5 years so that you will have $10,000 in 5 years. So insert 10000 as the Future Amount and 5 for Number of Periods. Assume an annual interest rate of 3.00% (insert 3 for Interest Rate per Period). The following table will determine the Annual Payment, which represents the annual payments that will accumulate to your future desired investment. If you input the numbers correctly, your Annual Payment is computed to be $1,884. Now revise the input to reflect your own desired savings amount in 5 years so that you can estimate how much you need to save per year to achieve your savings goal in 5 years. Compute Payment Needed to Achieve Future Amount Future Amount $20,000.00 Number of Periods 5.00 Interest Rate per Period 3.00% PMT = FV / [FV(R, N, -1)] Annual Payment $3,767
Decisions 1. Using the above formulas and understanding of the impact of interest rates and time on your savings, report on how much you must save per year and the return you must earn to meet your savings goal for graduation, and your savings goal in your first three years of post-graduation life.
I need a report on how much to save per year and the return to earn to meet savings goal for graduation, and savings goal in the first three years of post graduation. Can you please use the numbers above that are already calculated in the formula. I have had an answer on this below. I don't understand why the periods don't stay the same for 5 years. The annuity is 7964 I took that divided b y 60 = 132.7 per month and multiplied it by 12 for a year and got 1592.4. Is that the savings for the answer to saving for a year. IF not I need help figuring out the calculation for the return to meet after gradutaion and the next three years post graduation.
Goal 1 | Savings Goal for graduation, FV | $ 20,000 | |||||
Time till graduation (Number of periods) | 5 | ||||||
Present value of savings | $ - | ||||||
Expected interest rates | 3% | ||||||
Savings needed per year, PMT | $3,767.09 | =PMT(3%,5,0,20000,) | |||||
Goal 2 | Savings Goal for 1st year of post graduation, FV | $ 15,000 | |||||
Time till post graduation year 1 (Number of periods) | 6 | ||||||
Present value of savings | $ - | ||||||
Expected interest rates | 3% | ||||||
Savings needed per year, PMT | $2,318.96 | =PMT(3%,6,0,15000,) | |||||
Goal 3 | Savings Goal for 2nd year of post graduation, FV | $ 15,300 | |||||
Time till post graduation year 1 (Number of periods) | 7 | ||||||
Present value of savings | $ - | ||||||
Expected interest rates | 3% | ||||||
Savings needed per year, PMT | $1,996.75 | =PMT(3%,7,0,15300,) | |||||
Goal 4 | Savings Goal for 3rd year of post graduation, FV | $ 15,606 | |||||
Time till post graduation year 1 (Number of periods) | 8 | ||||||
Present value of savings | $ - | ||||||
Expected interest rates | 3% | ||||||
Savings needed per year, PMT | $1,754.99 | =PMT(3%,8,0,15606,) |
Part I:
Solve 4 of the following time value of money problems by filling inthe 4 columns to the right of the description.
Be sure to solve 1 problem from each of the following 4 categorieslisted under Problem Types. I have completed the first row as anexample.
Part II:
Discuss how you may use time value of money concepts in yourpersonal life. For example, saving for college tuition orretirement, paying off a car loan or home mortgage. Give specificdetails as to how you would use these formulas for more effectivedecision making. Create 1 description and fill in the table foryour 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 unclegive you now to finance four years of college, assuming an annualcost of $48,000 and an interest rate of 6% (applied to theprincipal until disbursed)? | Present Value of anordinary Annuity | PVAo | PV = 48,000(3.465) | $166,325.07 |
2 | How much interest would you earn ifyou deposited $300 at 6 percent for 27 months? | ||||
3 | If you deposit $2,000 in a 5-yearcertificate of deposit at 5.2%, how much will it be worth in fiveyears? | ||||
4 | How much interest would you pay toborrow $670 for eight months at 12 percent? | ||||
5 | You wish to borrow $18,000 to buy anew auto-mobile. Rate is 8.6% over five years with monthlypayments. Find the monthly payment. | ||||
6 | What is the future value of $800 at8 percent after six years? | ||||
7 | How much would you have in savingsif you kept $200 on deposit for eight years at 8% compoundedsemiannually? | ||||
8 | You choose to invest $50/month in a401(k) that invests in an international stock mutual fund. Assumingan annual rate of return of 9%, how much will this fund worth ifretiring in forty years? | ||||
9 | What is the future value of anannual deposit of $230 earning 6 percent for 15years? | ||||
10 | If you invest $600/Year in a 401(k)that invests in an international stock mutual fund. Assuming anannual rate of return of 9%, how much will this fund worth ifretiring in forty years? | ||||
11 | What amount would you have in aretirement account if you made annual deposits of $375 for 25 yearsearning 12 percent, compounded annually? | ||||
12 | What is the present value of $2,200earning 15 percent for eight years? | ||||
13 | How much money must you set asideat 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 childâseducation in 10 years, what amount should a parent deposit in asavings account that earns 12 percent, compoundedquarterly? | ||||
15 | If you deposit $2,000 in a 5-yearcertificate of deposit at 5.2% with quarterly compounding, how muchwill it be worth in five years? | ||||
16 | What is the present value of awithdrawal of $200 at the end of each year for 14 years with aninterest rate of 7 percent? | ||||
17 | How much would you have to depositnow to be able to withdraw $650 at the end of each year for 20years from an account that earns 11 percent? | ||||
18 | What would be the annual paymentamount for a $20,000, 10-year loan at 7 percent? |