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Exam 5: The Time Value of Money

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Question 1

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You borrow $25,000 to buy a car,and agree to make 48 monthly payments of $607.39 to repay the loan.What annual rate of interest,which is being compounded monthly,are you being charged?

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Question 2

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The same underlying formula is used for computing both the future value and present value.

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Question 3

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Jimmy just bought a new Ford SUV for his business.The price of the vehicle was $40,000.Jimmy made a $5,000 down payment and took out an amortized loan for the rest.The car dealership made the loan at 8% interest compounded monthly for five years.He is to pay back the principal and interest in equal monthly installments beginning one month from now.Determine the amount of Jimmy's monthly payment.

Bill saves $3,000 per year in his IRA starting at age 25 and continuing to age 65,when he retires.The amount Bill has in his IRA at age 65 can be characterized as the future value of an annuity.

What is the future value of $500 invested at 8.94% compounded quarterly for 12.5 years (rounded to nearest $1) ?

Today is your 20th birthday and your bank account balance is $25,000.Your account is earning 6.5% interest compounded semiannually.How much will be in the account on your 50th birthday?

It is your 6th birthday today.You have a trust fund with $50,000 that is earning 8% per year.You expect to withdraw $30,000 per year for 7 years starting on your 22nd birthday for graduate school.How much money will be left in the trust fund after your last withdrawal (rounded to the nearest $10) ?

You believe in the power of compounding and decide to save $1 per day by avoiding the purchase of a soda.You deposit the $1 at the end of each day in a bank account that pays 8% interest compounded daily.You are going to take a trip in 20 years with the money you have accumulated.How much money will you have in 20 years,assuming 365 days per year?

One bank offers you 4% interest compounded semiannually.What would the equivalent rate be if interest were compounded quarterly?

When repaying an amortized loan,the interest payments increase over time due to the compounding process.

The present value of a deferred annuity (e.g.,an annuity that starts 10 years from today)can be calculated in two steps: (1)calculate the future value of the annuity,and (2)calculate the present value of the amount determined in step (1).

An investment promises to pay you the following amounts at the end of each of the next 10 years: (1)$1,000,(2)$2,000,(3)$3,000,(4)$4,000,(5)- (10)$5,000 per year.If you want to earn a return of 8% per year,how much will you be willing to pay for the investment today?

You estimate you'll need $200,000 per year for 25 years starting on your 65th birthday to live on during your retirement.Today is your 50th birthday and you want to make equal deposits into an account paying 9% interest per year,the first deposit today and the last deposit on your 64th birthday.How much must each deposit be (rounded to the nearest $10) ?

John has to pay $1,000 per month for his mortgage for another 5 years,but he is considering paying the mortgage off in one lump sum.John cannot calculate the present value of the payments using the annuity formulas because his payments are monthly and not once per year.

Auto Loans R Them loans you $24,000 for four years to buy a car.The loan must be repaid in 48 equal monthly payments.The annual interest rate on the loan is 9 percent.What is the monthly payment?

A bond maturing in 10 years pays $80 each year (including year 10) and $1,000 upon maturity.Assuming 10 percent to be the appropriate discount rate,the present value of the bond is

If you want to have $12,500 in 57 months,how much money must you put in a savings account today? Assume that the savings account pays 4.5% and it is compounded quarterly; round to nearest $1.

If you invest $750 every six months at 8 percent compounded semiannually,how much would you accumulate at the end of 10 years?

A retirement home in Florida costs $200,000 today.Housing prices in Florida are increasing at a rate of 4% per year.Joe wants to buy the home in 8 years when he retires.Joe has $25,000 right now in a savings account paying 8% interest per year.Joe wants to make eight equal annual deposits into the savings account starting today.How much must each deposit be so Joe will have enough money in his savings account to buy the retirement home when he retires?

You have $25,000 in an investment account today.How much will be in the account in 30 years if the account earns (a)8% per year,(b)8% compounded semiannually,(c)8% compounded quarterly,(d)8% compounded monthly,and (e)8% compounded daily? Comment on the effect of more frequent compounding.