Question 1

Which of the following statements is CORRECT?

Accepted Answer

Time lines can be constructed to visualize cash flows regardless of whether they occur annually or more frequently. Additionally, time lines can accommodate unequal payments and not just annuities. Therefore, statement E is the only correct option.

Question 2

Suppose you are buying your first home for $145,000, and you have $15,000 for your down payment. You have arranged to finance the remainder with a 30-year, monthly payment, amortized mortgage at a 6.5% nominal interest rate, with the first payment due in one month. What will your monthly payments be?

Accepted Answer

$\begin{array}{l}
\begin{array} { l c } 
\text { Years } & 30 \mathrm {~N} \
\text { Payments/year } & 12\text { Periodic rate } \
\text { Nominal rate } & 6.50 \% \mathrm {PV} \
\text { Purchase price } & \$ 145,000 \mathrm { FV } \
\text { Down payment } & \$ 15,000 \mathrm { MT }
\end{array}
\begin{array} { r } 
360 \
0.54 \% \
\$ 130,000 \
\$ 0.00 \
\$ 821.69
\end{array}
\end{array}$

Question 3

Which of the following statements regarding a 15-year (180-month) $225,000, fixed-rate mortgage is CORRECT? (Ignore taxes and transactions costs.)

Accepted Answer

a is the correct answer. Thinking through the question, the other answers can all be eliminated. One could also set up an amortization schedule to prove that only statement a is correct.

Question 4

Your business has just taken out a 1-year installment loan for $72,500 at a nominal rate of 11.0% but with equal end-of-month payments. What percentage of the 2nd monthly payment will go toward the repayment of principal?

Accepted Answer

$\begin{array}{ll}
\text { N } & 12 \
\text { rNOM } & 11.0 \% \
\text { Per } . r & 0.9167 \% \
\text { PV } & \$ 72,500 \
\text { PMT } & \$ 6,407.67 \
\text { FV } & \$ 0 \% \text { prin. }=\operatorname{Prin} 2 / \text { PMT }=90.45 \%
\end{array}$ 
Amortization schedule (first 4 months)
 
$\begin{array}{l}
\begin{array} { l } 
\text { Month} &\text { Beg. Balance } &\text { Payment } \
1& 72,500.00 &  6,407.67 \
2&66,756.91 &  6,407.67 \
3&60,961.18 & 6,407.67 \
4&55.112 .32 &  6,407.67
\end{array}
\begin{array} { l } 
\text { Interest } &\text { Principal } &\text { End. Balance} \
664.58 & 5,743.09 & 66,756.91 \
611.94 & 5,795.73 & 60,961.18 \
558.81 & 5,848.86 & 55,112.32 \
505.20 & 5.902 .47 & 49,209.85
\end{array}
\end{array}$

Question 5

Your aunt wants to retire and has $375,000. She expects to live for another 25 years and to earn 7.5% on her invested funds. How much could she withdraw at the end of each of the next 25 years and end up with zero in the account?

Accepted Answer

$\begin{array}{lr}
\text { N } & 25 \
\text { I/YR } & 7.5 \% \
\text { PV } & \$ 375,000 \
\text { FV } & \$ 0.00 \
\text { PMT } & \$ 33,641.50
\end{array}$

Question 6

Which of the following statements regarding a 20-year monthly payment amortized mortgage with a nominal interest rate of 10% is CORRECT?

Accepted Answer

c is correct. b is clearly wrong, as are d and e. It is not obvious whether a is correct or not, but we could set up an example to see:
 $\begin{array} { l ll } 
\text { Loan } & 100000 \text { Term } & 20 \
\text { Rate } & 10\% \text { Periods/Year } & 12 \
\text { Periodic rate } & 0.00833333 \text { Total periods } & 140
\end{array}$ 
 $\begin{array} { l ll} 
\text { Payment } & - \$ 965.02 \text { Interest Month } 1 & \$ 833.33 \
\text { Interest as } \% \text { of total payment: } & 86 \% , \text { which is much larger than } 10 \%
\end{array}$

Question 7

Which of the following statements is CORRECT?

Accepted Answer

Time lines are useful for visualizing complex problems prior to doing actual calculations, as they provide a clear and organized representation of the cash flows over time. They can include both annuity payments and uneven amounts, and do not require all cash flows to occur annually. Additionally, they can be constructed for annuities where the payments occur at the beginning or end of the periods, as long as the timing of the payments is taken into account.

Question 8

Your bank offers to lend you $100,000 at an 8.5% annual interest rate to start your new business. The terms require you to amortize the loan with 10 equal end-of-year payments. How much interest would you be paying in Year 2?

Accepted Answer

Find the required payment:
 $\begin{array}{ll}
\text { N } & 10 \
\text { I } & 8.5 \% \
\text { PV } & \$ 100,000 \
\text { FV } & \$ 0 \
\text { PMT } & \$ 15,241 \text { Found with a calculator or Excel }
\end{array}$ 
Amortization schedule (first 2 years)
 $\begin{array}{ccccc}
\text { Year} &\text { Beg. Balance } &\text { Payment } &\text { Interest } &\text { Principal } &\text { End. Balance} \
1&100,000 & 15,241 & 8,500 & 6,741 & 93,259 \
2&93,259 & 15,241 & 7,927 & 7.314 & 85,945
\end{array}$

Question 9

Suppose you borrowed $12,000 at a rate of 9.0% and must repay it in 4 equal installments at the end of each of the next 4 years. How large would your payments be?

Accepted Answer

$\begin{array} { l l } 
\text { Years } = \mathrm { N } & 4 \
\text { I/YR } & 9.0 \% \
\mathrm { FV } & \$ 0 \
\text { Amourt borrowed } = \mathrm { PV } & \$ 12,000 \
\text { Payments } = \text { PMT } & \$ 3,704.02 \text { Fourd with a calculator, as the PMT }
\end{array}$

Question 10

Your cousin will sell you his coffee shop for $250,000, with "seller financing," at a 6.0% nominal annual rate. The terms of the loan would require you to make 12 equal end-of-month payments per year for 4 years, and then make an additional final (balloon) payment of $50,000 at the end of the last month. What would your equal monthly payments be?

Accepted Answer

Monthly annuity, so interest must be calculated on a monthly basis.
 $\begin{array} { lll } 
\text { Years } & 4 \text { Paymerts/year } & 12 \
\text { N } & 48 \mathrm { Norninal } \text { rate } & 6.0 \% \
\text { PV } & \$ 250,0001 / \text { period } & 0.5 \% \
\text { FV } & \$ 50,000 \mathrm { PMT } & \$ 4,947.01
\end{array}$

Question 11

Suppose you borrowed $15,000 at a rate of 8.5% and must repay it in 5 equal installments at the end of each of the next 5 years. How much would you still owe at the end of the first year, after you have made the first payment?

Accepted Answer

$\begin{array}{ll}
\text { Interest rate}& 8.5 \% \
\text { Years}& 5\
\text { Amount, borrowed}&\$ 15,000
\end{array}$ 
 $\begin{array} { l l l } 
\text { Step 1: } & \text { Find the PMT } & \$ 3,806.49 \
\text { Step 2: } & \text { Find the 1 st year's interest } & \$ 1,275.00 \
\text { Step 3: } & \text { Subtract the interest from the payment; this is repayment of } & \$ 2,531.49 \
& \text { principal } &  \
\text { Step 4: } & \text { Subtract the repayment of principal from the begirrning arnount } &\$ 12,468.51
\end{array}$

Question 12

Which of the following statements is CORRECT?

Accepted Answer

Time lines can be constructed to deal with situations where some of the cash flows occur annually but others occur quarterly. Time lines are a graphical tool used to visualize and analyze cash flows over time, and they can be used for annuities with equal or unequal payments, as well as for other types of cash flows, such as investments or loans. It is not necessary for all cash flows to occur annually or for them to be part of an annuity. Ordinary annuities are the most common type of annuity, but time lines can also be constructed for annuities due, where payments occur at the beginning of the periods.

Question 13

Your aunt wants to retire and has $375,000. She expects to live for another 25 years, and she also expects to earn 7.5% on her invested funds. How much could she withdraw at the beginning of each of the next 25 years and end up with zero in the account?

Accepted Answer

BEGIN Mode
 $\begin{array}{ll}
\text { N } & 25 \
\text { I/YR } & 7.5 \% \
\text { PV } &\$ 375,000 \
\text { FV } &  \$ 0.00  \
\text { PMT } & \$ 31,294.42
\end{array}$

Question 14

Suppose you earned a $275,000 bonus this year and invested it at 8.25% per year. How much could you withdraw at the end of each of the next 20 years?

Accepted Answer

$\begin{array}{lr}
\text { N } & 20 \
\text { I/YR } & 8.25 \% \
\text { PV } & \$ 275,000 \
\text { FV } & \$ 0.00 \
\text { PMT } & \$ 28,532
\end{array}$

Question 15

Suppose you borrowed $15,000 at a rate of 8.5% and must repay it in 5 equal installments at the end of each of the next 5 years. By how much would you reduce the amount you owe in the first year?

Accepted Answer

$\begin{array}{ll}
\text { Interest rate}& 8.5 \% \
\text { Years}& 5\
\text { Amount, borrowed}&\$ 15,000
\end{array}$ 
 $\begin{array} { l l l } 
\text { Step 1: } & \text { Find the PMT } & 3,806.49 \
\text { Step 2: } & \text { Find the } 1 \text { st year's interest } & 1,275.00 \
\text { Step 3: } & \text { Subtract the interest from the payment; this is repayment of } & 2,531.49 \
& \text { principal } &
\end{array}$

Question 16

On January 1, 2016, your sister's pet supplies business obtained a 30-year amortized mortgage loan for $250,000 at a nominal annual rate of 7.0%, with 360 end-of-month payments. The firm can deduct the interest paid for tax purposes. What will the interest tax deduction be for 2016?

Accepted Answer

$\begin{array} { l c r } 
\text { Years } & \text { 30Norninal r } & 7.00 \% \
\text { Periods/yr } & 12 \mathrm { I /} \text { period } & 0.5833 \% \
\text { N (12mo) } & 360 P \mathrm { MT } & \$ 1,663.26 \
\text { PV } = \text { Loan } & \$ 250,000 \text { Interest, } 2016 & \$ 17,419.55 \
\text { FV } & \$ 0 &
\end{array}$ 
Amortization schedule (first 3 months)
 $\begin{array} { c c c c c c } 
\text { Year } &\text { Beg. Balance } &  \text { Payment }  &  \text { |nterest } &  \text { Principal } & \text { End. Balance } \
1& 250,000.00&1,663.26&1,458.33 &204.92& 249,795.08\
2 & 249,795.08 & 1,663.26 & 1,457.14 & 206.12 & 249,588.96 \
3 & 249,588.96 & 1,663.26 & 1,455.94 & 207.32 & 249,381.64 \
4 & 249,381.64 & 1,663.26 & 1,454.73 & 208.53 & 249,173.11 \
5 & 249,173.11 & 1,663.26 & 1,453.51 & 209.75 & 248,963.36 \
6 & 248,963.36 & 1,663.26 & 1,452.29 & 210.97 & 248,752.39 \
7 & 248,752.39 & 1,663.26 & 1,451.06 & 212.20 & 248,540.19 \
8 & 248,540.19 & 1,663.26 & 1,449.82 & 213.44 & 248,326.75 \
9 & 248,326.75 & 1,663.26 & 1,448.57 & 214.68 & 248,112.07 \
10 & 248,112.07 & 1,663.26 & 1,447.32 & 215.94 & 247,896.13 \
11 & 247,896.13 & 1,663.26 & 1,446.06 & 217.20 & 247,678.94 \
12 & 247,678.94 & \underline { 1,663.26 } &  \underline { 1,444.79}& \underline { 218.46 } & 247,460.48\
&&19.959 .07 & 17.419 .55 & 2.539 .52
\end{array}$

Question 17

You plan to borrow $35,000 at a 7.5% annual interest rate. The terms require you to amortize the loan with 7 equal end-of-year payments. How much interest would you be paying in Year 2?

Accepted Answer

Find the required payment:
 $\begin{array} { l l } 
\text { N} & 7 \
\text { I } & 7.5 \% \
\text {PV } & \$ 35,000 \
\text { FV } & \$ 0 \
\text { PMT } & 6,608.01 \text { Found with a calculator or Excel }
\end{array}$ 
Amortization schedule (first 2 years)
 $\begin{array}{llllll}
\text { Year} &\text { Beg. Balance } &\text { Payment } &\text { Interest } &\text { Principal } &\text { End. Balance} \
1 & 35,000.00 & 6,608.01 & 2,625.00 & 3,983.01 & 31,016.99 \
2 & 31.016 .99 & 6.608 .01 & 2,326.27 & 4.281 .74 & 26.735 .25
\end{array}$

Question 18

Suppose you borrowed $14,000 at a rate of 10.0% and must repay it in 5 equal installments at the end of each of the next 5 years. How much interest would you have to pay in the first year?

Accepted Answer

$\begin{array} { l l } 
\text { I/YR } & 10.0 \% \
\text { Years } & 5 \
\text { Amount borrowed } & \$ 14,000 \
\text { Interest in Year 1 } & \$ 1,400.00 \text {, Sirmply rmultiply the rate tirnes the arnount borrowed}
\end{array}$

Question 19

Which of the following statements regarding a 30-year monthly payment amortized mortgage with a nominal interest rate of 8% is CORRECT?

Accepted Answer

c is correct. b is clearly wrong, as are d and e. It is not obvious whether a is correct or not, but we could set up an example to see:
 $\begin{array} { l ll } 
\text { Loan } & 100000 \text { Term } & 30 \
\text { Rate } & 8 \% \text { Periods/Year } & 12 \
\text { Periodic rate } & 0.00666666667 \text { Total periods } & 360
\end{array}$ 
 $\begin{array} { l r r } 
\text { Payment } & - \$ 733.76 \text { Interest, Month } 1 & \$ 666.67 \
\text { Interest as \% of total \#360 payment: } & 1 \% \text { Irterest, Month } 360 & \$ 7.25 \
\text { Principal as \% of total \#360 payment } & 99 \% \text { Principal, Month } 360 & \$ 726.51
\end{array}$

Question 20

Which of the following statements is CORRECT?

Accepted Answer

Time lines can be constructed for annuities where the payments occur at either the beginning or the end of the periods. Statement A is incorrect as cash flows can be uneven amounts. Statement B is incorrect as time lines can be used for any frequency of cash flows. Statement C is incorrect as time lines are useful for visualizing problems before doing calculations. Statement D is incorrect as time lines can be constructed for any frequency of cash flows.

Quiz 28: Time Value of Money

Which of the following statements is CORRECT?

Which of the following statements regarding a 15-year (180-month) $225,000, fixed-rate mortgage is CORRECT? (Ignore taxes and transactions costs.)

Your business has just taken out a 1-year installment loan for $72,500 at a nominal rate of 11.0% but with equal end-of-month payments. What percentage of the 2nd monthly payment will go toward the repayment of principal?

Your aunt wants to retire and has $375,000. She expects to live for another 25 years and to earn 7.5% on her invested funds. How much could she withdraw at the end of each of the next 25 years and end up with zero in the account?

Which of the following statements regarding a 20-year monthly payment amortized mortgage with a nominal interest rate of 10% is CORRECT?

Which of the following statements is CORRECT?

Your bank offers to lend you $100,000 at an 8.5% annual interest rate to start your new business. The terms require you to amortize the loan with 10 equal end-of-year payments. How much interest would you be paying in Year 2?

Suppose you borrowed $12,000 at a rate of 9.0% and must repay it in 4 equal installments at the end of each of the next 4 years. How large would your payments be?

Suppose you borrowed $15,000 at a rate of 8.5% and must repay it in 5 equal installments at the end of each of the next 5 years. How much would you still owe at the end of the first year, after you have made the first payment?

Which of the following statements is CORRECT?

Your aunt wants to retire and has $375,000. She expects to live for another 25 years, and she also expects to earn 7.5% on her invested funds. How much could she withdraw at the beginning of each of the next 25 years and end up with zero in the account?

Suppose you earned a $275,000 bonus this year and invested it at 8.25% per year. How much could you withdraw at the end of each of the next 20 years?

Suppose you borrowed $15,000 at a rate of 8.5% and must repay it in 5 equal installments at the end of each of the next 5 years. By how much would you reduce the amount you owe in the first year?

On January 1, 2016, your sister's pet supplies business obtained a 30-year amortized mortgage loan for $250,000 at a nominal annual rate of 7.0%, with 360 end-of-month payments. The firm can deduct the interest paid for tax purposes. What will the interest tax deduction be for 2016?

You plan to borrow $35,000 at a 7.5% annual interest rate. The terms require you to amortize the loan with 7 equal end-of-year payments. How much interest would you be paying in Year 2?

Suppose you borrowed $14,000 at a rate of 10.0% and must repay it in 5 equal installments at the end of each of the next 5 years. How much interest would you have to pay in the first year?

Which of the following statements regarding a 30-year monthly payment amortized mortgage with a nominal interest rate of 8% is CORRECT?

Which of the following statements is CORRECT?