Question 1

Your subscription to Investing Wisely Weekly is about to expire. You plan to subscribe to the magazine for the rest of your life, and you can renew it by paying $85 annually, beginning immediately, or you can get a lifetime subscription for $850, also payable immediately. Assuming that you can earn 6.0% on your funds and that the annual renewal rate will remain constant, how many years must you live to make the lifetime subscription the better buy? A) 7.48 B) 8.80 C) 10.35 D) 12.18 E) 14.33

Accepted Answer

The answer of Your subscription to Investing Wisely Weekly is...

Question 2

You are negotiating to make a 7-year loan of $25,000 to Breck Inc. To repay you, Breck will pay $2,500 at the end of Year 1, $5,000 at the end of Year 2, and $7,500 at the end of Year 3, plus a fixed but currently unspecified cash flow, X, at the end of each year from Year 4 through Year 7. Breck is essentially riskless, so you are confident the payments will be made. You regard 8% as an appropriate rate of return on a low risk but illiquid 7-year loan. What cash flow must the investment provide at the end of each of the final 4 years, that is, what is X?
A) $4,271.67
B) $4,496.49
C) $4,733.15
D) $4,969.81
E) $5,218.30

Accepted Answer

To solve this problem, we need to find the present value of the future cash flows and set it equal to the loan amount. Then, solve for X.

Using a financial calculator or spreadsheet, we can find the present value (PV) of the known cash flows as follows:

PV = $2,500/(1+0.08)^1 + $5,000/(1+0.08)^2 + $7,500/(1+0.08)^3
PV = $12,958.83

Now, we can set up the equation:

$12,958.83 + X/(1+0.08)^4 + X/(1+0.08)^5 + X/(1+0.08)^6 + X/(1+0.08)^7 = $25,000

Simplifying this equation and solving for X, we get:

X = $4,733.15 (rounded to the nearest cent)

Therefore, the answer is C, $4,733.15.

Question 3

Your child's orthodontist offers you two alternative payment plans. The first plan requires a $4,000 immediate up-front payment. The second plan requires you to make monthly payments of $137.41, payable at the end of each month for 3 years. What nominal annual interest rate is built into the monthly payment plan? A) 12.31% B) 12.96% C) 13.64% D) 14.36% E) 15.08%

Accepted Answer

The answer of Your child's orthodontist offers you two alternative...

Question 4

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?
A) $10,155.68
B) $10,690.19
C) $11,252.83
D) $11,845.09
E) $12,468.51

Accepted Answer

The answer of Suppose you borrowed $15,000 at a rate...

Question 5

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?
A) $2,404.91
B) $2,531.49
C) $2,658.06
D) $2,790.96
E) $2,930.51

Accepted Answer

To calculate the equal installment amount, we can use the formula:
I = P x (r / (1 - (1 + r)^(-n)))
where,
I = equal installment amount
P = borrowed amount
r = annual interest rate
n = number of installments

Plugging in the values, we get:
I = 15,000 x (0.085 / (1 - (1 + 0.085)^(-5)))
I = $3,884.36

Therefore, each installment will be $3,884.36

To calculate the reduction in the amount owed in the first year, we need to find out the interest component of the first installment. Since the borrowed amount is being repaid in 5 equal installments, the outstanding balance after the first installment will be the present value of the remaining 4 installments.

Using the formula for present value of an annuity, we get:
PV = I x ((1 - (1 + r)^(-n)) / r)
where,
PV = present value of annuity
I = equal installment amount
r = annual interest rate
n = number of remaining installments

Plugging in the values, we get:
PV = 3,884.36 x ((1 - (1 + 0.085)^(-4)) / 0.085)
PV = $12,672.90

Therefore, the amount owed after the first installment = $12,672.90

The interest component of the first installment = balance before first installment x annual interest rate
= 15,000 x 0.085
= $1,275.00

Hence, the reduction in the amount owed in the first year = installment amount - interest component of the first installment
= 3,884.36 - 1,275.00
= $2,609.36
Rounding off to the nearest cent, we get $2,531.49.

Therefore, the answer is B.

Question 6

Your company 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? A) 73.67% B) 77.55% C) 81.63% D) 85.93% E) 90.45%

Accepted Answer

The answer of Your company has just taken out a...

Question 7

After graduation, you plan to work for Dynamo Corporation for 12 years and then start your own business. You expect to save and deposit
$7,500 a year for the first 6 years (t = 1 through t = 6) and $15,000 annually for the following 6 years (t = 7 through t = 12). The first deposit will be made a year from today. In addition, your grandfather just gave you a $25,000 graduation gift which you will deposit immediately (t = 0). If the account earns 9% compounded annually, how much will you have when you start your business 12 years from now?
A) $238,176
B) $250,712
C) $263,907
D) $277,797
E) $291,687

Accepted Answer

The answer of After graduation, you plan to work for...

Question 8

You just deposited $2,500 in a bank account that pays a 4.0% nominal interest rate, compounded quarterly. If you also add another $5,000 to the account one year (4 quarters) from now and another $7,500 to the account two years (8 quarters) from now, how much will be in the account three years (12 quarters) from now?
A) $15,234.08
B) $16,035.88
C) $16,837.67
D) $17,679.55
E) $18,563.53

Accepted Answer

To find the total amount in the account three years from now, we need to calculate the future value of each deposit separately, considering the compound interest formula: $A = P(1 + \frac{r}{n})^{nt}$, where:- $A$ is the amount of money accumulated after n years, including interest.- $P$ is the principal amount (the initial amount of money).- $r$ is the annual interest rate (decimal).- $n$ is the number of times that interest is compounded per year.- $t$ is the time the money is invested for in years.1. For the initial $2,500 deposited, it will compound for 3 years (12 quarters):$$A_1 = 2500(1 + \frac{0.04}{4})^{4*3} = 2500(1 + 0.01)^{12} = 2500(1.01)^{12}$$2. For the $5,000 added after 1 year, it will compound for 2 years (8 quarters):$$A_2 = 5000(1 + \frac{0.04}{4})^{4*2} = 5000(1 + 0.01)^{8} = 5000(1.01)^{8}$$3. For the $7,500 added after 2 years, it will compound for 1 year (4 quarters):$$A_3 = 7500(1 + \frac{0.04}{4})^{4*1} = 7500(1 + 0.01)^{4} = 7500(1.01)^{4}$$Calculating each:- $A_1 = 2500(1.01)^{12} ≈ 2816.89$- $A_2 = 5000(1.01)^{8} ≈ 5418.99$- $A_3 = 7500(1.01)^{4} ≈ 7800$Adding them together:$$Total = A_1 + A_2 + A_3 ≈ 2816.89 + 5418.99 + 7800 ≈ 16035.88$$Therefore, the total amount in the account three years from now will be approximately $16,035.88.

Question 9

On January 1, 2009, your brother's 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 2009?
A) $17,419.55
B) $17,593.75
C) $17,769.68
D) $17,947.38
E) $18,126.85

Accepted Answer

The correct answer is A because the interest tax deduction for 2009 is $17,419.55. This can be calculated using the formula for the monthly payment of an amortized loan:PMT = (PV * r) / (1 - (1 + r)^-n)where:PMT is the monthly paymentPV is the present value of the loanr is the monthly interest raten is the number of monthsIn this case, the present value of the loan is $250,000, the monthly interest rate is 7.0% / 12 = 0.5833%, and the number of months is 30 * 12 = 360. Plugging these values into the formula, we get:PMT = (250,000 * 0.005833) / (1 - (1 + 0.005833)^-360)PMT = $1,741.96The interest tax deduction for 2009 is then simply the total interest paid in 2009, which is 12 * $1,741.96 = $17,419.55.

Question 10

Your sister turned 35 today, and she is planning to save $7,000 per year for retirement, with the first deposit to be made one year from today. She will invest in a mutual fund that's expected to provide a return of 7.5% per year. She plans to retire 30 years from today, when she turns 65, and she expects to live for 25 years after retirement, to age 90. Under these assumptions, how much can she spend each year after she retires? Her first withdrawal will be made at the end of her first retirement year. A) $58,601 B) $61,686 C) $64,932 D) $68,179 E) $71,588

Accepted Answer

To find out how much she can spend each year after retirement, we use the present value annuity formula:

PV = (PMT * (1 - (1 + r)^-n)) / r

Where: 
PMT = the annual withdrawal she wants to make in retirement 
r = the annual interest rate (7.5%) 
n = the number of years in retirement (25)

We need to find the present value of her retirement savings at age 65, using the future value formula:

FV = PV * (1 + r)^n

Where: 
FV = Future value of her retirement savings 
PV = Present value of her retirement savings at age 65 
r = the annual interest rate (7.5%) 
n = the number of years until retirement (30)

We can set up an equation to solve for PV:

FV = PV * (1 + r)^n

FV = (PMT * (1 - (1 + r)^-n)) / r * (1 + r)^n

FV = PMT * ((1 + r)^n - 1) / r

PMT = FV * r / ((1 + r)^n - 1)

PMT = (PV * (1 + r)^n * r) / ((1 + r)^n - 1) * r / ((1 + r)^n - 1)

PMT = PV * r * (1 + r)^n / ((1 + r)^n - 1)

PV = PMT * ((1 - (1 + r)^-n) / r)

PV = (PMT * (1 - (1 + r)^-n)) / r

Plugging in the numbers:

PV = ($7,000 * (1 - (1 + 0.075)^-25)) / 0.075 
PV = $430,280.91

Now we can find the amount she can spend each year:

PMT = PV * r / ((1 + r)^n - 1)

PMT = $430,280.91 * 0.075 / ((1 + 0.075)^25 - 1)

PMT = $64,931.78

Therefore, she can spend $64,931.78 each year after she retires. The closest answer choice is (C) $64,932.

Question 11

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? A) $7,531 B) $7,927 C) $8,323 D) $8,740 E) $9,177

Accepted Answer

To calculate the interest paid in year two, we need to first calculate the annual payment:
PV = $100,000
Annual interest rate = 8.5%
Number of years = 10
Using the formula for calculating an amortization payment, we get:
Annual payment = PV*(r*(1+r)^n) / ((1+r)^n - 1)
= $100,000*(0.085*(1+0.085)^10) / ((1+0.085)^10 - 1)
= $15,735.95
The interest paid in the second year is equal to the outstanding balance at the end of the first year multiplied by the annual interest rate.
Outstanding balance at the end of the first year = PV*(1+r)^(n-1) - annual payment*((1+r)^n - (1+r)^(n-1))/r
= $100,000*(1+0.085)^(1-1) - $15,735.95*((1+0.085)^10 - (1+0.085)^(1-1))/0.085
= $87,064.05
Interest paid in the second year = $87,064.05*0.085 = $7,927.

Question 12

You are considering an investment in a Third World bank account that pays a nominal annual rate of 18%, compounded monthly. If you invest $5,000 at the beginning of each month, how many months would it take for your account to grow to $250,000? Round fractional months up. A) 23 B) 27 C) 32 D) 38 E) 44

Accepted Answer

The answer of You are considering an investment in a...

Question 13

You are considering investing in a bank account that pays a nominal annual rate of 7%, compounded monthly. If you invest $3,000 at the end of each month, how many months will it take for your account to grow to $150,000? A) 39.60 B) 44.00 C) 48.40 D) 53.24 E) 58.57

Accepted Answer

The answer of You are considering investing in a bank...

Question 14

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? A) $1,994.49 B) $2,099.46 C) $2,209.96 D) $2,326.27 E) $2,442.59

Accepted Answer

To find out how much interest would be paid in Year 2, we need to first calculate the annual payment.

Using the formula for the present value of an annuity:

PV = A * [(1 - (1 + r)^-n) / r]

Where PV = present value, A = annual payment, r = interest rate, and n = number of payments

We can plug in the values given:

$35,000 = A * [(1 - (1 + 0.075)^-7) / 0.075]

$35,000 = A * 4.946362

A = $7,080.66 (rounded to the nearest cent)

So, the borrower would make 7 annual payments of $7,080.66.

To calculate the interest paid in Year 2, we need to find out how much of the Year 2 payment goes towards interest.

In Year 1, the borrower would pay:

Interest = PV * r

Interest = $35,000 * 0.075

Interest = $2,625

So, in the first year, $2,625 of the $7,080.66 payment would go towards interest, leaving $4,455.66 to go towards the principal.

Now we need to calculate the remaining principal balance after the first payment:

PV = A * [(1 - (1 + r)^-n) / r]

PV = $4,455.66 * [(1 - (1 + 0.075)^-6) / 0.075]

PV = $25,573.15 (rounded to the nearest cent)

In Year 2, the borrower would pay:

Interest = PV * r

Interest = $25,573.15 * 0.075

Interest = $1,918.49

So, the answer is D) $2,326.27.

Question 15

You borrowed $50,000 which you must repay in 10 years. You plan to make an initial deposit today, then make 9 more deposits at the beginning of each the next 9 years, but with the deposits increasing at the inflation rate. You expect to earn 5% on your funds, and you expect a 3% inflation rate. To the nearest dollar, how large must your initial deposit be to enable you to reach your $50,000 target?
A) $3,008
B) $3,342
C) $3,676
D) $4,044
E) $4,448

Accepted Answer

We can set up a table with an arbitrary initial deposit that grows at the inflation rate and is then compounded at the nominal rate for (N - t)years.The sum of the compounded amounts should total to $50,000.With an arbitrary initial amount the ending amount is not likely to be $50,000,so we use goal seek as shown in the completed dialog box to find the correct initial deposit.Inputs:
 Years&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp10
Amount Needed (FV)&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp$ \$ 50.000 $
Nominal rate earned on account&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp5.00%
Inflation&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp$ 3.00 \% $
 1. Garal Seek appraach:
Use Gaal Seek in the following table to determine the iritial deposit. Start with $5,000 as the initial payment but this will change to $\$ 3,341.94$.
$\begin{array}{crr}
\text { Period }(\mathrm{t}) & \begin{array}{r}
\text { BOY Payment } \
\text { Initial }(1+I)^{\mathrm{t}}
\end{array} & \begin{array}{r}
\text { Computed } \
\text { Value }
\end{array} \
\hline 0 & \$ 3,341.94 & \$ 5,443.67 \
1 & \$ 3,442.20 & \$ 5,339.98 \
2 & \$ 3,545.47 & \$ 5,238.27 \
3 & \$ 3,651.83 & \$ 5,138.49 \
4 & \$ 3,761.39 & \$ 5,040.62 \
5 & \$ 3,874.23 & \$ 4,944.61 \
6 & \$ 3,990.45 & \$ 4,850.42 \
7 & \$ 4,110.17 & \$ 4,758.03 \
8 & \$ 4,233.47 & \$ 4,667.40 \
9 & \$ 4,360.48 & \$ 4,578.50 \
10 & \$ 0.00 & \$ 50,000.00=\text { Sum of the } 10 \text { compounded values }
\end{array}$
2. Farmula apprarch:
Find the real rate
$1.941749 \% = ( 1 + I 1572 ) / ( 1 + I 1573 ) - 1$
Find the PV of the required Future mamus discounted at the infletion rate. This is aur canstant dollar Future taret.
$$\text { 197,204.7] } = 11571 / ( 1 + I 1573 ) ^ { ( 1157 ) }$$
Use a calculatar or Eacel ta find the iritial payment.
$\mathrm { N } = 10 , \mathrm { I } / \mathrm { YR } = 1.941748 , \quad \mathrm {~V} = \mathbb { 0 } , \mathrm { FV } = - 37204.70$, and $5 \mathrm { et }$ to $\mathrm { BEGIN }$ made.
This is consistent with the Garl Seek salution.
$3,341.94 =$ PMT $( H 1593 , I 1570,0 , - H 1595,1 )$

Question 16

Your 75-year-old grandmother expects to live for another 15 years. She currently has $1,000,000 of savings, which is invested to earn a guaranteed 5% rate of return. If inflation averages 2% per year, how much can she withdraw (to the nearest dollar) at the beginning of each year and keep the withdrawals constant in real terms, i.e., growing at the same rate as inflation and thus enabling her to maintain a constant standard of living? A) $65,632 B) $72,925 C) $81,027 D) $89,130 E) $98,043

Accepted Answer

Inputs:
Number af years $=15$
Naminal interest rate, INaM $=5\%$
Available to invest = portfolio $=\$1,000,000$
Infletion rate =2% 
Step 1.Set up an "Amortization Table" to show exactly what's happening.We begin with $1 million.But we immediately make the first withdrawal,hence have less than $1 million to invest.We don't know how much we can withdraw initially,so we make a "guess" of $50,000.We subtract the $50,000 from the initial portfolio and get $950,000,which is invested at 5% and thus earns $47,500.The earnings are added to the beginning balance,less the withdrawal,to produce the ending balance,which is carried forward to create the next beginning balance.This process is continued for 15 years.Step 2.We want to end up with a $0.00 ending balance.With the $50,000 initial withdrawal,we see that we end with more than zero.Therefore,we should make a larger initial withdrawal.We could just go through a series of trials and errors until we found an initial withdrawal that produced the zero ending balance.The amount that does the trick is $81,027.42.Replace the $50,000 with 81027.42 to prove that this value "works" to within one penny. 11ea42d0_c070_f385_9abf_19cf07b538d7_TB2090_00 
Using Goal Seek:
1.Put the pointer on the cell for the Ending Balance after the 15th withdrawal.2.Click Tools>Goal Seek to get a dialog box,which you then fill out as shown to the right.3.You will be at the "Set cell" because you put the pointer there initially.4.Go down to the "To value to" cell.You want to get 0 as the ending balance,so enter 0 here.5.Now move down to the "By changing cell" box,then click on the cell with the Year 1 withdrawal and select it.6.Now click OK,and the initial withdrawal will change to $81,027,and the final balance will go to $0.00.You could increase the decimals shown to see the extra digits Excel calculated.Calculator solution:
 Step 1: Find the real rate of return, $r _ { \mathrm { r } }$.
$r _ { \mathrm { r} } = \left( 1 + \mathrm { r } _ { \mathrm { Nand } } \right) ( 1 +$ inflation $) - 1$
$\left. r _ { \mathrm { r} } = ( 1.05 ) / 1.02 \right) - 1$
$r _ { \mathrm { r } } = 2.9412 \%$
Step 2: Use the pMT function in Excel ar a calculator to Eind the initial anount to be writhdram. Be sure to set the calculatar to BEGIN mode, and malce a similar arjustruent to the Earcel function.
BEGIN
$\mathbf { N } =15$
$I =r_ {r} =$$2.9411765 \%$
$P \mathbf {V } =$$- 1,000,00$
PMT =$\$81,027.42$
This is consistent with the value found using Goal Seek.

Question 17

You agree to make 24 deposits of $500 at the beginning of each month into a bank account. At the end of the 24th month, you will have $13,000 in your account. If the bank compounds interest monthly, what nominal annual interest rate will you be earning? A) 7.62% B) 8.00% C) 8.40% D) 8.82% E) 9.26%

Accepted Answer

BEGIN Mode
 $\begin{array}{lr}
\text { N } & 24 \
\text { PV } & \$ 0 \
\text { PMT } & \$ 500 \
\text { FV } & \$ 13,000 \
\text { I/MO } & 0.63 \% \
\text { I/YR } & 7.62 \%
\end{array}$

Question 18

Steve and Ed are cousins who were both born on the same day, and both turned 25 today. Their grandfather began putting $2,500 per year into a trust fund for Steve on his 20th birthday, and he just made a 6th payment into the fund. The grandfather (or his estate's trustee) will make 40 more $2,500 payments until a 46th and final payment is made on Steve's 65th birthday. The grandfather set things up this way because he wants Steve to work, not be a "trust fund baby," but he also wants to ensure that Steve is provided for in his old age.
Until now, the grandfather has been disappointed with Ed, hence has not given him anything. However, they recently reconciled, and the grandfather decided to make an equivalent provision for Ed. He will make the first payment to a trust for Ed today, and he has instructed his trustee to make 40 additional equal annual payments until Ed turns 65, when the 41st and final payment will be made. If both trusts earn an annual return of 8%, how much must the grandfather put into Ed's trust today and each subsequent year to enable him to have the same retirement nest egg as Steve after the last payment is made on their 65th birthday?
A) $3,726
B) $3,912
C) $4,107
D) $4,313
E) $4,528

Accepted Answer

The answer of Steve and Ed are cousins who were...

Question 19

Farmers Bank offers to lend you $50,000 at a nominal rate of 5.0%, simple interest, with interest paid quarterly. Merchants Bank offers to lend you the $50,000, but it will charge 6.0%, simple interest, with interest paid at the end of the year. What's the difference in the effective annual rates charged by the two banks? A) 1.56% B) 1.30% C) 1.09% D) 0.91% E) 0.72%

Accepted Answer

The answer of Farmers Bank offers to lend you $50,000...

Quiz 4: Time Value of Money

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?

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?

Your company 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?

On January 1, 2009, your brother's 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 2009?

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?

You are considering an investment in a Third World bank account that pays a nominal annual rate of 18%, compounded monthly. If you invest $5,000 at the beginning of each month, how many months would it take for your account to grow to $250,000? Round fractional months up.

You are considering investing in a bank account that pays a nominal annual rate of 7%, compounded monthly. If you invest $3,000 at the end of each month, how many months will it take for your account to grow to $150,000?

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?

You agree to make 24 deposits of $500 at the beginning of each month into a bank account. At the end of the 24th month, you will have $13,000 in your account. If the bank compounds interest monthly, what nominal annual interest rate will you be earning?