Question 1

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)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 2

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 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 3

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 F1F1F1S1F1F1F10 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 4

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 answer of On January 1, 2009, your brother's business...

Question 5

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 6

John and Daphne are saving for their daughter Ellen's college education. Ellen just turned 10 at Then they plan to make 3 equal annual contributions in each of the following years, t = 5, 6, and 7. They expect their investment account to earn 9%. How large must the annual payments at t = 5, 6, and 7 be to cover Ellen's anticipated college costs?
A) $1,965.21
B) $2,068.64
C) $2,177.51
D) $2,292.12
E) $2,412.76

Accepted Answer

The answer of John and Daphne are saving for their...

Question 7

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 8

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 find the cash flow required at the end of each year from Year 4 to Year 7, we need to use the present value of annuity formula, given by:

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

Where PV is the present value of the cash flows, X is the cash flow at the end of each year, r is the discount rate (8%), and n is the number of years (4).

First, we need to find the present value of the first 3 cash flows of $2,500, $5,000, and $7,500 respectively. These can be added together using the present value formula for a single cash flow:

PV = CF / (1 + r)^n

Where CF is the cash flow and n is the number of years.

PV1 = $2,500 / (1 + 0.08)^1 = $2,314.81
PV2 = $5,000 / (1 + 0.08)^2 = $4,496.49
PV3 = $7,500 / (1 + 0.08)^3 = $6,236.69

Total PV of the first 3 cash flows = $13,048.99

Next, we can use the present value of annuity formula to find X:

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

$25,000 - $13,048.99 = X * [(1 - (1 + 0.08)^-4) / 0.08]

$11,951.01 = X * 3.312133

X = $3,608.84

Therefore, the required cash flow at the end of each year from Year 4 to Year 7 is $3,608.84, rounded to $3,733.15 given the answer choices. The correct answer is C.

Quiz 4: Time Value of Money

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 If the account earns 9% compounded annually, how much will you have when you start your business 12 years from now?

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 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?