Question 1

What is the expected real rate of interest for an account that offers a 12 percent nominal rate of return when the rate of inflation is 6 percent annually?

Accepted Answer

To calculate the expected real rate of interest, we subtract the inflation rate from the nominal rate of return. Therefore, the expected real rate of interest for this account is 12% - 6% = 6%. However, we need to adjust for the effects of inflation on the purchasing power of our money, so we need to calculate the inflation-adjusted return.

The formula for calculating the inflation-adjusted return is: 
(1 + nominal rate) / (1 + inflation rate) - 1

Using the values given in the question: 
(1 + 0.12) / (1 + 0.06) - 1 = 0.0566 or 5.66%

Therefore, the expected real rate of interest for this account is 5.66%. The best choice is B.

Question 2

What is the minimum nominal rate of return should you accept, if you require a 4 percent real rate of return and the rate of inflation is expected to average 3.5 percent during the investment period?

Accepted Answer

The nominal rate of return can be calculated using the Fisher equation: (1 + nominal rate) = (1 + real rate) * (1 + inflation rate). Plugging in the values: (1 + nominal rate) = 1.04 * 1.035 = 1.0764, which gives a nominal rate of approximately 7.64 percent.

Question 3

Approximately how much must be saved for retirement in order to withdraw $100,000 per year for the next 25 years if the balance earns 8 percent annually, and the first payment occurs one year from now?

Accepted Answer

The present value of an annuity formula is used to calculate how much needs to be saved. The formula is PV = PMT x [(1 - (1 + r)^-n) / r], where PMT is the annual withdrawal, r is the interest rate, and n is the number of years. Plugging in the values: PV = $100,000 x [(1 - (1 + 0.08)^-25) / 0.08] gives approximately $1,067,000.

Question 4

Which of the following characteristics applies to the amortization of a loan such as a home mortgage?

Accepted Answer

The answer of Which of the following characteristics applies to...

Question 5

Which of the following statements best describes the real interest rate?

Accepted Answer

Real interest rates take into account the inflation rate, so they can be negative if the inflation rate is higher than the nominal interest rate, zero if the inflation rate and nominal interest rate are equal, or positive if the nominal interest rate is higher than the inflation rate.

Question 6

Appleton University seeks to setup a scholarship for its students in perpetuity.Every six months, $5,000 will be provided to students.If interest is 4.8% compounded monthly, determine the amount that must be invested in order to deliver on the semi-annual scholarship.

Accepted Answer

The amount that must be invested can be calculated using the formula:PV = PMT * [1 - (1 + r/n)^(-nt)] / (r/n)where:PV is the present value of the investmentPMT is the semi-annual scholarship amount ($5,000)r is the annual interest rate (4.8%)n is the number of compounding periods per year (12)t is the number of years the scholarship will be provided in perpetuity (infinite)Plugging in the values, we get:PV = 5000 * [1 - (1 + 0.048/12)^(-12*t)] / (0.048/12)PV = 5000 * [1 - (1.004)^(-12*t)] / 0.004PV = 5000 * [1 - 0] / 0.004PV = 5000 / 0.004PV = $206,260Therefore, the amount that must be invested in order to deliver on the semi-annual scholarship is $206,260.

Question 7

Which of the following strategies will allow real retirement spending to remain approximately equal, assuming savings of $1,000,000 invested at 8 percent, a 25-year horizon, and 4 percent expected inflation?

Accepted Answer

Spending approximately $63,000 annually will allow real retirement spending to remain approximately equal, assuming savings of $1,000,000 invested at 8 percent, a 25-year horizon, and 4 percent expected inflation.

Question 8

What will be the monthly payment on a home mortgage of $75,000 at 12 percent interest, to be amortized over 30 years?

Accepted Answer

The monthly payment can be calculated using the formula for a fixed-rate mortgage: PMT = [P * r * (1 + r)^n] / [(1 + r)^n – 1], where P is the principal ($75,000), r is the monthly interest rate (12% annual interest rate divided by 12 months = 0.01), and n is the total number of payments (30 years * 12 months = 360). Using this formula, the monthly payment is approximately $771.46.

Question 9

Assume your uncle recorded his salary history during a 40-year career and found that it had increased ten-fold.If inflation averaged 5 percent annually during the period, how would you describe his purchasing power, on average?

Accepted Answer

Since the salary increased ten-fold, it means that it increased by a factor of 10. To find the average annual increase, we can take the 10th root of this factor, which is approximately 1.16. This means that, on average, the salary increased by 16% per year.

If inflation averaged 5% annually during the period, it means that prices increased by an average of 5% per year. Therefore, the uncle's purchasing power would have decreased by 5% each year due to inflation.

To determine how much he "beat" inflation, we can subtract the inflation rate from the average annual increase in the salary:

16% - 5% = 11%

Therefore, the uncle's purchasing power increased by an average of 11% per year, which is almost 1% above the inflation rate. So the correct answer is B.

Question 10

The present value of an annuity stream of $100 per year is $614 when valued at a 10 percent rate.By approximately how much would the value change if these were annuities due?

Accepted Answer

The value of an annuity due is equal to the value of an ordinary annuity plus one payment. Therefore, the value of the annuity due would be $675 ($614 + $61). So the value would increase by $61.

Question 11

Your real estate agent mentions that homes in your price range require a payment of approximately $1,200 per month over 30 years at 9 percent interest.What is the approximate size of the mortgage with these terms?

Accepted Answer

The present value of the mortgage can be calculated using the formula:PV = PMT * [(1 - (1 + r)^-n) / r]where:PV is the present value of the mortgagePMT is the monthly paymentr is the monthly interest raten is the number of monthsIn this case, we have:PMT = $1,200r = 9% / 12 = 0.0075n = 30 * 12 = 360Plugging these values into the formula, we get:PV = $1,200 * [(1 - (1 + 0.0075)^-360) / 0.0075]PV = $1,200 * [1 - (1.0075)^-360] / 0.0075PV = $1,200 * [1 - 0.2486] / 0.0075PV = $1,200 * 0.7514 / 0.0075PV = $128,035.20Therefore, the approximate size of the mortgage with these terms is $128,035.

Question 12

Your retirement account has a current balance of $50,000.What interest rate would need to be earned in order to accumulate a total of $1,000,000 in 30 years, by adding $6,000 annually?

Accepted Answer

To find the interest rate needed, we use the future value of an annuity formula combined with the future value of a lump sum. After calculations, the required interest rate is approximately 7.24 percent.

Question 13

How much must be saved annually, beginning one year from now, in order to accumulate $50,000 over the next 10 years, earning 9 percent annually?

Accepted Answer

The correct answer is A.The future value of the annuity is $50,000. The interest rate is 9%. The number of years is 10. The present value of the annuity is $3,291.

Question 14

If inflation in Wonderland averaged about 20% per month in 2008, what was the annual inflation rate?

Accepted Answer

To calculate the annual inflation rate, we need to use the formula (1 + monthly inflation rate)^12 - 1. Plugging in 20% as the monthly inflation rate, we get (1 + 0.2)^12 - 1 = 7.9 or 790%. Therefore, the answer is C.

Question 15

How much must be deposited today in an account earning 6 percent annually to accumulate a 20 percent down payment to use in purchasing a car one year from now, assuming that the car's current price is $20,000, and inflation will be 4 percent?

Accepted Answer

The down payment needed for the car is 20% of $20,000, which is $4,000.

Since inflation is 4%, we need to factor in the future value of money. In other words, the amount we need in one year will be worth 4% more than it is today.

Therefore, the amount we need to deposit today is:

PV = $4,000 / (1 + 0.04) = $3,846.15

However, we also need to factor in the interest earned on the account, which is 6%.

So, the amount we need to deposit today is:

PV = $3,846.15 / (1 + 0.06) = $3,625

Therefore, the answer is choice C, $3,925. This is the closest option to our calculated amount of $3,625.

Question 16

What happens over time to the real cost of purchasing a home, if the mortgage payments are fixed in nominal terms and inflation is in existence?

Accepted Answer

The answer of What happens over time to the real...

Question 17

Approximately how much should be accumulated by the beginning of retirement to provide a $2,500 monthly check that will last for 25 years, during which time the fund will earn 8 percent interest with monthly compounding?

Accepted Answer

We can use the present value formula for an annuity due to calculate the required savings:
PV = PMT x [(1 - (1 + r/n)^-nt) / (r/n)] x (1+r/n)
where PV is the present value, PMT is the monthly payment, r is the annual interest rate, n is the number of compounding periods per year, and t is the total number of periods.
Substituting the given values, we get:
PV = $2,500 x [(1 - (1 + 0.08/12)^(-25*12)) / (0.08/12)] x (1+0.08/12)
PV = $2,500 x 129.515
PV = $323,787.50
So, the required savings at retirement should be approximately $323,800. Therefore, the best choice is B.

Question 18

You're ready to make the last of four equal, annual payments on a $1,000 loan with a 10 percent interest rate.If the amount of the payment is $315.47, how much of that payment is accrued interest?

Accepted Answer

The accrued interest for the last payment is calculated on the remaining principal after the third payment. The principal at the start of the fourth year is $286.79, and 10% of this is $28.68, which is the interest portion of the final payment.

Question 19

Considering the past economic history of Canada, high rates of price inflation are typically accompanied by:

Accepted Answer

High rates of price inflation are typically accompanied by high nominal interest rates in Canada. The central bank may increase the policy interest rate in order to control inflation by making borrowing more expensive and reducing demand in the economy. This can lead to higher nominal interest rates in the market as well.

Question 20

With $1.5 million in an account expected to earn 8 percent annually over the retiree's 30 years of life expectancy, what annual annuity can be withdrawn, beginning today?

Accepted Answer

The answer of With $1.5 million in an account expected...

Quiz 5: The Time Value of Money