Question 1

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?
A) The real cost is constant.
B) The real cost is increasing.
C) The real cost is decreasing.
D) The price index must be known to answer this question.

Accepted Answer

When mortgage payments are fixed in nominal terms, inflation reduces the real value of these payments over time, effectively decreasing the real cost of purchasing a home.

Question 2

If $120,000 is borrowed for a home mortgage,to be repaid at 9% interest over 30 years with annual payments of $11,680.36,how much interest (as opposed to return of capital)is paid in the last year of the loan?
A) $120,000
B) $162,000
C) $181,458
D) $227,598

Accepted Answer

Value of loan at start of last year = $11,680.36 / 1.09 = $10,715.93Interest on loan in last year = 0.09 × $10,715.93 = $964.43

Question 3

How much must be saved at the end of each year for the next 10 years in order to accumulate $50,000,if you can earn 9% annually? Assume you contribute the same amount to your savings every year.
A) $3,291.00
B) $3,587.87
C) $4,500.33
D) $4,587.79

Accepted Answer

Payment = $50,000 / [(1.09¹⁰ − 1) / 0.09]Payment = $3,291.00

Question 4

You have just retired with savings of $1.5 million.If you expect to live for 30 years and to earn 8% a year on your savings,how much can you afford to spend each year? Assume that you spend the money at the start of each year.
A) $112,148.50
B) $120,000.00
C) $123,371.44
D) $133,241.15

Accepted Answer

$1,500,000 = Pmt_OA {(1 / 0.08) − [1 / 0.08(1.08)³⁰]}PMT_OA = $133,241.15PMT_AD = PMT_OA/ (1 + r)PMT_AD = $133,241.15 / 1.08PMT_AD = $123,371.44

Question 5

How much can be accumulated for retirement if $2,000 is put aside at the end of each of the next 40 years? Assume that you can earn 9% a year on your savings.
A) $87,200.00
B) $675,764.89
C) $736,583.73
D) $802,876.27

Accepted Answer

FV = $2,000 {[(1 + 0.09)⁴⁰ − 1] / 0.09}FV = $675,764.89

Question 6

What will be the monthly payment on a $75,000 30-year home mortgage at 1% interest per month?
A) $771.46
B) $775.90
C) $1,028.61
D) $1,034.53

Accepted Answer

Payment = $75,000 / [(1 / 0.01) − 1 / 0.01(1.01)³⁶⁰]Payment = $771.46

Question 7

What is the expected real rate of interest for an account that offers a 12% nominal rate of return when the rate of inflation is 6% annually?
A) 5.00%
B) 5.66%
C) 6.00%
D) 9.46%

Accepted Answer

1 + real interest rate = (1 + nominal interest rate) / (1 + inflation)1 + real interest rate = 1.12 / 1.06Real interest rate = 5.66%

Question 8

Real interest rates:
A) always exceed inflation rates.
B) can decline to zero but no lower.
C) can be negative, zero, or positive.
D) traditionally exceed nominal rates.

Accepted Answer

Real interest rates can be negative when inflation exceeds the nominal interest rate. They can also be zero or positive depending on the inflation and nominal interest rate. Therefore, option C is the correct answer.

Question 9

The present value of an annuity stream of $100 per year is $614 when valued at a 10% rate.By approximately how much would the value change if these were annuities due?
A) $10
B) $61.40
C) $10 ×Number of years in annuity stream
D) $6.14 × Number of years in annuity stream

Accepted Answer

PV_{Annuity due} = PV _{ordinary annuity} × (1 + r)Difference = $614(1.1) − $614 = $61.40

Question 10

If inflation in Wonderland was 3% per month in 2016,what was the annual rate of inflation?
A) 36.00%
B) 42.58%
C) 40.09%
D) 41.27%

Accepted Answer

(1.03)¹² − 1 = 0.4258, or 42.58%

Question 11

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% annually,and the first payment occurs one year from now?
A) $1,067,477.62
B) $1,128,433.33
C) $1,487,320.09
D) $1,250,000.00

Accepted Answer

PV = $100,000 {(1 / 0.08) − [1 / 0.08(1.08)²⁵]}PV = $1,067,477.62

Question 12

$50,000 is borrowed,to be repaid in three equal,annual payments with 10% interest.Approximately how much principal is amortized with the first payment?
A) $2,010.60
B) $5,000.00
C) $15,105.74
D) $20,105.74

Accepted Answer

Payment = $50,000 / [1 / 0.1 − 1 / 0.1(1.1)³]Payment = $20,105.74Principal payment = $20,105.74 − ($50,000 × 0.1)Principal payment = $15,105.74

Question 13

Your real estate agent mentions that homes in your price range require a payment of $1,200 per month for 30 years at 0.75% interest per month.What is the size of the mortgage with these terms?
A) $128,035.05
B) $147,940.29
C) $149,138.24
D) $393,120.03

Accepted Answer

PV = $1,200[(1 / 0.0075) − 1 / 0.0075(1.0075)³⁶⁰]PV = $149,138.24

Question 14

An amortizing loan is one in which:
A) the principal remains unchanged with each payment.
B) accrued interest is paid regularly.
C) the maturity of the loan is variable.
D) the principal balance is reduced with each payment.

Accepted Answer

An amortizing loan is one in which the principal balance is reduced with each payment. This means that a portion of each payment goes towards paying off the principal amount borrowed, as well as the interest that has accrued on the balance. This process continues until the loan is fully paid off.

Question 15

On the day you retire you have $1,000,000 saved.You expect to live another 25 years during which time you expect to earn 6.19% on your savings while inflation averages 2.5% annually.Assume you want to spend the same amount each year in real terms and die on the day you spend your last dime.What real amount will you be able to spend each year?
A) $61,334.36
B) $79,644.58
C) $79,211.09
D) $61,931.78

Accepted Answer

Real rate = (1.0619 / 1.025) − 1 = 0.036$1,000,000 = PMT {(1 / 0.036) − [1 / 0.036(1.036)²⁵]}PMT = $61,334.36

Question 16

Assume you are making $989 monthly payments on your amortized mortgage.The amount of each payment that is applied to the principal balance:
A) decreases with each succeeding payment.
B) increases with each succeeding payment.
C) is constant throughout the loan term.
D) fluctuates monthly with changes in market interest rates.

Accepted Answer

In an amortized mortgage, the portion of each payment that goes towards the principal increases over time, while the portion that goes towards interest decreases.

Question 17

Your retirement account has a current balance of $50,000.You plan to add $6,000 a year to the account for each of the next 30 years.Use a financial calculator or Excel to find what interest rate you need to earn in order to have $1,000,000 in the account at the end of the 30 years.?
A) 5.02%
B) 7.24%
C) 9.80%
D) 10.07%

Accepted Answer

Financial calculator: n = 30; PV = −50,000; PMT = −6,000; FV = 1,000,000; CPT i = 7.24%, orExcel function Rate(nper, PMT, PV, FV)

Question 18

You're ready to make the last of four equal,annual payments on a $1,000 loan with a 10% interest rate.If the amount of the payment is $315.47,how much of that payment is accrued interest?
A) $28.68
B) $31.55
C) $100.00
D) $315.47

Accepted Answer

$315.47 − ($315.47 / 1.1) = $28.68

Question 19

Assume your uncle recorded his salary history during a 40-year career and found that it had increased 10-fold.If inflation averaged 4% annually during the period,then over his career his purchasing power:
A) remained on par with inflation.
B) increased by nearly 1% annually.
C) increased by nearly 2% annually.
D) decreased.

Accepted Answer

FV = PV(1 + r)^t10 = 1(1 + i)⁴⁰r = 5.93%Real rate = (1.0593 / 1.04) − 1 = 0.0186, or 1.86%

Question 20

How much do you need when you retire to provide a $2,500 monthly check that will last for 25 years? Assume that your savings can earn 0.5% a month.
A) $361,526.14
B) $388,017.16
C) $402,766.67
D) $414,008.24

Accepted Answer

Monthly interest rate = 0.06 / 12 = 0.005PV = $2,500 {(1 / 0.005) − [1 / 0.005(1.005)^{12 × 25}]}PV = $388,017.16

Quiz 5: The Time Value of Money

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?

If $120,000 is borrowed for a home mortgage,to be repaid at 9% interest over 30 years with annual payments of $11,680.36,how much interest (as opposed to return of capital) is paid in the last year of the loan?

How much must be saved at the end of each year for the next 10 years in order to accumulate $50,000,if you can earn 9% annually? Assume you contribute the same amount to your savings every year.

You have just retired with savings of $1.5 million.If you expect to live for 30 years and to earn 8% a year on your savings,how much can you afford to spend each year? Assume that you spend the money at the start of each year.

How much can be accumulated for retirement if $2,000 is put aside at the end of each of the next 40 years? Assume that you can earn 9% a year on your savings.

What will be the monthly payment on a $75,000 30-year home mortgage at 1% interest per month?

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

Real interest rates:

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

If inflation in Wonderland was 3% per month in 2016,what was the annual rate of inflation?

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% annually,and the first payment occurs one year from now?

$50,000 is borrowed,to be repaid in three equal,annual payments with 10% interest.Approximately how much principal is amortized with the first payment?

Your real estate agent mentions that homes in your price range require a payment of $1,200 per month for 30 years at 0.75% interest per month.What is the size of the mortgage with these terms?

An amortizing loan is one in which:

Assume you are making $989 monthly payments on your amortized mortgage.The amount of each payment that is applied to the principal balance:

Your retirement account has a current balance of $50,000.You plan to add $6,000 a year to the account for each of the next 30 years.Use a financial calculator or Excel to find what interest rate you need to earn in order to have $1,000,000 in the account at the end of the 30 years.?

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

Assume your uncle recorded his salary history during a 40-year career and found that it had increased 10-fold.If inflation averaged 4% annually during the period,then over his career his purchasing power:

How much do you need when you retire to provide a $2,500 monthly check that will last for 25 years? Assume that your savings can earn 0.5% a month.