using the annuityformula:
F = (Pn/r)[(1 + (r/n))nt+1 â 1]
where:
F is the future value of ALL of theinvestments/loans, including interest.
⢠P is the principal amount invested or paid at the beginning ofeach period.
⢠r is the annual interest rate, written as a decimal (ex: 6%=.06).
⢠n is the number of times that interest is compounded peryear.
⢠t is the number of years the money is invested orborrowed.
Suppose you invest P at the beginning of each month in aretirement account in hopes to save $600,000 for retirement at theage of 65. For both the annual rates r = 3.2% and r = 8.05%,compounded monthly, find the amount of money you will need toinvest per month:
A. if you start this process as soon as you turn 23 (so youinvest for 42 years total).
B. if you start this process as soon as you turn 30 (so youinvest for 35 years total).
C. if you start this process as soon as you turn 40 (so youinvest for 25 years total).
using the annuityformula:
F = (Pn/r)[(1 + (r/n))nt+1 â 1]
where:
F is the future value of ALL of theinvestments/loans, including interest.
⢠P is the principal amount invested or paid at the beginning ofeach period.
⢠r is the annual interest rate, written as a decimal (ex: 6%=.06).
⢠n is the number of times that interest is compounded peryear.
⢠t is the number of years the money is invested orborrowed.
Suppose you invest P at the beginning of each month in aretirement account in hopes to save $600,000 for retirement at theage of 65. For both the annual rates r = 3.2% and r = 8.05%,compounded monthly, find the amount of money you will need toinvest per month:
A. if you start this process as soon as you turn 23 (so youinvest for 42 years total).
B. if you start this process as soon as you turn 30 (so youinvest for 35 years total).
C. if you start this process as soon as you turn 40 (so youinvest for 25 years total).
Related questions
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? |
