Finance 320 - Ch. 5 Quiz

You want to purchase a new condominium that costs $325,000. Your plan is to pay 20 percent down in cash and finance the balance over 15 years at 4.1 percent APR. What will be your monthly mortgage payment including principal and interest?

$1936.24 The loan amount = Home value minus down payment = $325,000 - 0.2*$325,000 = $260,000. This loan will be repaid on a monthly basis over 15 years. So, the number of periods = 12*15 = 180. The APR = 4.1%. So the monthly interest rate = 4.1%/12 (take care to not round off this calculation). What we are calculating is the payment. PV = -$260,000 I% = 4.1/12 N = 180 Compute PMT = 1936.24

You plan to save $200 a month for the next 24 years and hope to earn an average rate of return of 10.6 percent. How much more will you have at the end of the 24 years if you invest your money at the beginning rather than the end of each month?

$2317.82 This problem requires us to first calculate the FV of an ordinary annuity, then the FV of its corresponding annuity due and then take the difference. Ordinary annuity FV can be computed as: N =24*12 = 288, PMT = $200, I% = 10.6/12, FV = ? $262,394.25 For the annuity due, we let the money compound for one more period, so $262,394.25*(1+0.106/12) = $264,712.069 The difference is $2,317.82

At the end of this month, Les will start saving $200 a month for retirement through his company's retirement plan. His employer will contribute an additional $.50 for every $1.00 that he saves. If he is employed by this firm for 30 more years and earns an average of 8.25 percent on his retirement savings, how much will he have in his retirement account 30 years from now?

$470465.70 This problem requires us to calculate the future value of an ordinary annuity. The payment = $200 + 0.5*$200 = $300. N= 360 months (30 years). I% = 8.25/12. FV =? The FV comes out to be $470,465.70

The manager of Steve's Audio has approved Daisy's application for 24 months of credit with maximum monthly payments of $45. If the APR is 19.2 percent, what is the maximum initial purchase that Daisy can make on credit?

$890.99 In this situation we are given the monthly payment ($45) Daisy can make and the number of months (24). To calculate the credit that Steve's Audio can give Daisy we need to calculate the PV of the annuity. Before we do that, we need to get the monthly rate from the APR. That would be APR/12 = 1.6%. Now, we have all the info to get the PV of the annuity. PMT (C) = $45 I% = 1.6 N = 24 Calculate PV = $890.99

You are considering an investing with a quoted return of 10% per year. If interest is compounded daily, what is the effective annual return on this investment?

10.52% To get the EAR, we just calculate the return we get by investing a single dollar. PV = -$1 N = 365 (days) I% = 10/365 FV = ? = $1.105155. So we made a return of 10.5155 cents on the dollar = 10.52%

You just received an offer in the mail to transfer the $5,000 balance from your current credit card, which charges an annual rate of 18.7 percent, to a new credit card charging a rate of 7.9 percent. You plan to make payments of $250 a month on this debt. How many fewer payments will you have to make to pay off this debt if you transfer the balance to the new card?

2.63 payments In this situation, we need to do two calculations of the number of periods as above. Note that both the rates are quoted rates, i.e., APRs. So be sure to convert to monthly rates in the usual way (dividing by 12). If you do not transfer: PMT = $250 I% = 18.7/12 N = ? PV = -$5000 The number of periods comes out to be = 24.15 If you do transfer: PMT = $250 I% = 7.9/12 N = ? PV = -$5000 The number of periods comes out to be = 21.51

Today, you borrowed $6,200 on your credit card to purchase some furniture. The interest rate is 14.90 percent APR, compounded monthly. How long will it take you to pay off this debt assuming that you do not charge anything else and make regular monthly payments of $120?

6.93 years In this situation, we are given the monthly payment you can make ($120) and the amount of credit you have taken ($6,200). We also know that the APR is 14.90%. So, the monthly rate is 14.90%/12. So, we have all the info to get the number of periods for the annuity. PMT = $120 I% = 14.90 N = ? PV = -$6,200 The number of periods comes out to be = 83.135 months = 83.135/12 = 6.93 years

Recently, you needed money and agreed to sell a car you had inherited. You sold it at a price of $55,000, and allowed the buyer to pay for it in monthly payments of $1,500 for 42 months. What interest rate (APR) did you charge the buyer?

7.78 percent In this situation, we are given the monthly payment the buyer can make ($1,500) and the number of months (42). We also know that you agreed on a price today of $55,000 (present value). So, we have all the info to get the discount rate of the annuity. PMT = $1500 I% = ? N = 42 PV = -$55,000 The monthly interest rate comes out to be = 0.6497% Therefore, APR = 0.6497%*12 = 7.776%

Which of the following statements related to annuities and perpetuities is correct?

A perpetuity composed of $100 monthly payments is worth more than an annuity of $100 monthly payments; given equal discount rates. A perpetuity of cash flows is always worth more than a similar annuity because it has more payments.

Which one of the following compounding periods will yield the lowest effective annual rate given a state future value at year 5 and an annual percentage rate of 10%?

Annual To get the lowest EAR, we would want the interest to compound the least frequently. Conversely, to get the highest EAR, we would want the interest to compound most frequently. Continuous compounding is the most frequent way of compounding where interest compounds every fraction of a second.

Assume all else is equal. When comparing savings accounts, you should select the account that has the:

Highest effective annual rate. We always want the highest rate when saving (and the lowest rate when borrowing). A high APR does not automatically imply a good deal because the compounding frequency could be low. A high EAR assures us the best annual rate of return for your money and must be chosen.

You are comparing two investment options that each pay 6% interest, compounded annually. Option A pays $2000 the first year followed by two annual payments of $5000 each. Option B pays three annual payments of $4000 each. Which one of the following statements is correct given these two investment options? Assume a positive discount rate.

Option B has a higher present value. In Option B by the end of year 1, $4000 is accumulating interest (whereas in A it is only $2000). By end of year 2, in Option B $8000 of principal is accumulating interest (whereas in A it is only $7000). Further, Option B has more interest accumulated from year 1. By end of year 3, both options have $12000 of principle accumulating interest, but Option B has much more interest accumulated, so B will always have a higher future and present value.

Chris has three options for settling an insurance claim. Option A will provide $1,500 a month for 6 years. Option B will pay $1,025 a month for 10 years. Option C offers $85,000 as a lump sum payment today. The applicable discount rate is 6.8 percent, compounded monthly. Which option should Chris select, and why, if he is only concerned with the financial aspects of the offers?

Option B: It has the largest value today. Option A and Option B are monthly annuities. We need to calculate the PV of each and compare it to $85,000 and choose the highest of the three numbers. Option A has a PV of $88,479.22 Option B has a PV of $89,068.22 Therefore B, is the best (because it has the largest PV)

Chandler Tire Co. is trying to decide which one of two projects it should accept. Both projects have the same start-up costs. Project 1 will produce annual cash flows of $52000 a year for 6 years. Project 2 will produce cash flows of $48000 a year for eight years. The company requires a 15% rate of return. Which project should the company select and why?

Project 2, because the present value of the cash inflows exceeds those of Project 1 by $18598.33 In this situation, we need to calculate the present value of each project (each is an annuity) and compare. We pick the one with the higher value. Project 1: PV of annuity = $196793.100 Project 2: PV of annuity = $215391.432 Difference = $18598.33

Christie is buying a new car today and is paying a $500 cash down payment. She will finance the balance at 6.3% interest. Her loan requires 36 equal monthly payments of $450 each with the first payment due 30 days from today. Which one of the following statements is correct concerning this purchase?

To compute the loan amount, you must use a monthly interest rate. The initial loan amount is nothing but the PV of the payments which are a monthly annuity, so we must use a monthly interest rate.