CH 5 HW

Lily invested $10,000 seven years ago with an insurance company that has paid her 4 percent (APR), compounded semi-annually (twice per year). How much interest did Lily earn over the 7 years?

$3,194.79 6-month rate = .04/2 = .02 number of 6-month periods = 7 x 2 = 14 FV= 10,000(1+.02)^14 = $13,194.79 Interest earned = $13,194,79 - 10,000 = $3,194.79

Suppose you postpone consumption and invest at 6% when inflation is 2%. What is the approximate real rate of your reward for saving?

1+.06/1+.02 -1 x100 = 4%

You are running short of cash and really need to pay your rent. A friend suggests that you check out the local title pawn shop. At the shop they offer to loan you $1,000 if you pay them back $1,200 in one week. It seems like a good idea to you because you don't want to sell your car and you are sure you will be able to pay the money back in a week. What is the APR on this loan?

1040% rate = (1,200- 1,000)/1,000 APR = m x r = 52 weeks x 20% = 1040%

You put 20% down on a home with a purchase price of $250,000. The down payment is thus $50,000, leaving a balance owed of $200,000. The bank will loan the remaining balance at 3.91% APR. You will make annual payments with a 30-year payment schedule. What is the annual annuity payment under this schedule?

200,000 = PMT [1-(1/(1+.0391)^30/.0391] = $11,439.96

Becky is seeking to expand her stamp collection. Each year, stamps increase in price at a seven percent rate. She believes that if she invests her money for one year, she should be able to buy 24 stamps for what 23 stamps would cost today. What is her real interest rate or reward for waiting?

4.35% 24/23 - 1 x 100

You are running short of cash and really need to pay your rent. A friend suggests that you check out the local title pawn shop. At the shop they offer to loan you $2,000 if you pay them back $2,200 in one week. It seems like a good idea to you because you don't want to sell your car and you are sure you will be able to pay the money back in a week. What is the APR on this loan?

520% rate = (2,200-2,000)/2,000 = .1 = 10% APR = m x r = 52 x 10% = 520%

Lily invested $10,000 five years ago with an insurance company that has paid her 4 percent (APR), compounded semi-annually (twice per year). How much interest did Lily earn over the 5 years?

6 month rate = .04/2 = .02 number of 6 month period = 5x2 = 10 FV =10,000(1+.02)^10 = 12,189.94 Interest earned = 12,189.94 - 10,000 = $2,189.94

Lily invested $10,000 ten years ago with an insurance company that has paid her 10 percent (APR), compounded semi-annually (twice per year). How much interest did Lily earn over the ten years?

6 month rate = .1/2 = .05 number of 6 month period = 10 x 2 = 20 FV = 10,000(1+.05)^20 = 26,532.98 - 10,000 = $16,533

Suppose you postpone consumption and invest at 9% when inflation is 2%. What is the approximate real rate of your reward for saving?

7% *r = 1+r/1+h -1 *r = 1+.09/1+.02 -1 x 100 = 6.86%

Suppose you postpone consumption and invest at 14% when inflation is 2%. What is the approximate real rate of your reward for saving?

= 1 + .14/ 1 + .02 - 1 x 100 = 11.7 = 12%

The actual rate paid or received after accounting for compounding is called the

Effective annual rate

The phrase "price to rent money" is sometimes used to refer to ________.

Interest Rates

The real rate is 1.25% and inflation is 5.25%. What is the approximate nominal rate?

Roughly speaking, the nominal rate is the real rate plus inflation. Thus, the nominal rate is 1.25% plus 5.25% equals 6.50%.

What is the EAR if the APR is 5% and compounding is quarterly?

Slightly above 5.09% Using the EAR formula, we get 5.0945%, or slightly above 5.09%. EAR = [(1 + APR/m)^m] -1 = [(1 + .05/4)^4] - 1 = 5.0945%.

What is the EAR if the APR is 10.52% and compounding is daily?

Using the EAR formula, we get 11.0916% or slightly above 11.09%. EAR = [(1 + APR/m)^m] -1 = [(1 + 0.1052/365)^365] -1 = 11.0916%.

What if Jennifer were to invest $2,750 today, compounded semiannually, with an annual interest rate of 5.25%. What amount of interest will Jennifer earn in one year?

With PV = $2,750, Rate =5.25%/2, Periods = 2, compounding semiannually solve for FV = $2,896.27. To solve for the interest earned use FV - PV = $2,896.27 - $2,750 = $146.27. FV=2,750(1+.0.2625)^2 = 2,896.27 - 2,750 = $146.27

A company selling a bond is ________ money.

borrowing

You put 20% down on a home with a purchase price of $250,000. The down payment is thus $50,000, leaving a balance owed of $200,000. A bank will loan you this remaining balance at 3.9% APR. You will make monthly end-of-the-period payments with a 30-year payment schedule. What is the monthly annuity payment under this schedule?

monthly rate = .039/12 = .00325 number of months = 30 x 12 = 360 200,000= [1-1/(1+.00325)^360/.00325] = $943.34

You just entered into a $150,000 30-year home mortgage at an annual interest rate of 4.25% making monthly payments of $737.91. Suppose you add an additional payment of $295.97 each month to the $737.91 house payment making your total monthly payments equal to $1,033.88. This extra amount is applied against the principal of the original loan. How long will it take you to pay off your loan of $150,000?

monthly rate = .0425/12 = .003541 It will take about 204 months. n=ln[1/(1-PV×r/PMT)]/ln(1+r) n=ln[1/(1-150,000x.003541/1,033.88)]/ln(1+.003541) = 204 months

Assume that Ray is 20 years old and has 45 years for saving until he retires. He expects an APR of 6% on his investments. How much does he need to save if he puts money away monthly in equal end-of-the-month amounts to achieve a future value of $2,000,000 dollars in 45 years' time?

monthly rate = .06/12 = .005 number of months = 45 x 12 = 540 2,000,000 = PMT [(1+.005)^540-1/.005] = $725.69

Assume you just bought a new car and now have a car loan to repay. The amount of the principal is $22,000, the loan is at 6% APR, and the monthly payments are spread out over 6 years. What is the monthly loan payment?

monthly rate = .06/12 = .005 number of months = 6 x 12 = 72 22,000 = PMT [1-1/(1+.005)^72/.005] = $364.60

Assume you just bought a new boat and now have a boat loan to repay. The amount of the principal is $68,000, the loan is at 6.75% APR, and the monthly payments are spread out over 7 years. What is the monthly loan payment?

monthly rate = .0675/12 = .005625 number of months = 7 x 12 = 84 68,000 = PMT [1-1/(1+.005625)^84/.005625] = $1,018.01

Assume that Ray is 38 years old and has 27 years for saving until he retires. He expects an APR of 7.5% on his investments. How much does he need to save if he puts money away monthly in equal end-of-the-month amounts to achieve a future value of $1,200,000 dollars in 27 years' time?

monthly rate = .075/12 = .00625 number of months = 27 x 12 =324 1,200,000 = PMT [(1+.00625)^324-1/.00625] = $1,148.81

Susan's goal is to retire with $500,000 in her retirement account. The local bank advertises an APR of 6% with monthly compounding on retirement fund accounts. If she retires in 30 years how much should Susan save each month to reach her goal?

monthly rate = 6%/12 = .005 number of months = 30 x 12 = 360 500,000 = PMT [(1+.005)^360 -1/.005] = $497.75

To determine the interest paid each compounding period, we take the advertised annual percentage rate and simply divide it by the ________ to get the appropriate periodic interest rate.

number of compounding periods per year

The number of periods for a consumer loan (n) is equal to the ________.

number of years times compounding periods per year

Kenna invests $5,000 today, compounded monthly, with an annual interest rate of 8.52%. What amount of interest will she earn in one year?

rate = .0852/12 = .0071 number of periods = 1 x 12 = 12 FV= 5,000(1+.0071)^12 = 5,443.04 - 5,000 = $443.04

The typical payments on a consumer loan are made at ________.

the end of each month

Assume that you are willing to postpone consumption today and buy a certificate of deposit (CD) at your local bank. Your reward for postponing consumption implies that at the end of the year ________.

you will be able to buy more goods or services