Question 1

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 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 (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

To solve this problem, we can use the formula for the future value of an annuity:

FV = PMT x [(1 + r)^n - 1]/r

where:
PMT = the annual deposit
r = the interest rate per period (we use 9%/year compounded annually, so r = 0.09/1 = 0.09)
n = the number of periods (we have two different periods, so we need to calculate them separately)

For the first six years (t = 1 through t = 6), we have:
PMT = $7,500
r = 0.09/1
n = 6

FV = $7,500 x [(1 + 0.09)^6 - 1]/0.09 = $61,345.81

For the following six years (t = 7 through t = 12), we have:
PMT = $15,000
r = 0.09/1
n = 6

FV = $15,000 x [(1 + 0.09)^6 - 1]/0.09 = $144,675.76

Now, we need to calculate the future value of the $25,000 graduation gift deposited immediately (t = 0):
PV = $25,000
r = 0.09/1
n = 12

FV = PV x (1 + r)^n = $25,000 x (1 + 0.09)^12 = $68,776.72

Finally, we need to calculate the total future value by adding up the three amounts:
Total FV = $61,345.81 + $144,675.76 + $68,776.72 = $274,798.29

Therefore, the answer is D) $277,797 (rounded to the nearest dollar).

Question 3

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 4

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

To solve this, we use the formula for the present value of an annuity that grows at the rate of inflation. The formula is PV = PMT * [(1 - (1 + g)^-n) / (r - g)], where PV is the present value ($1,000,000), PMT is the payment we want to find, g is the growth rate of the payment (inflation rate, 2%), r is the rate of return (5%), and n is the number of periods (15 years). Rearranging the formula to solve for PMT gives us the correct answer after plugging in the values.

Question 5

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 6

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 7

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

We can use the formula for calculating the payment of an installment loan:

Payment = A / ((1 - (1 + r)^(-n)) / r)

where A is the borrowed amount, r is the interest rate, and n is the number of payments.

In this case, A = $15,000, r = 8.5%, and n = 5.

Plugging in the values, we get:

Payment = 15,000 / ((1 - (1 + 0.085)^(-5)) / 0.085) = $3,971.98

So, each installment payment is $3,971.98.

To find out how much of the first payment goes towards reducing the principal amount, we can use the formula:

Interest = r x Remaining Balance

Principal Reduction = Payment - Interest

At the start of the first year, the remaining balance is $15,000.

So, Interest = 0.085 x 15,000 = $1,275

Principal Reduction = 3,971.98 - 1,275 = $2,696.98

Therefore, the amount reduced in the first year is $2,696.98, which is closest to option B ($2,531.49).

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 solve this, we use the formula for compound interest for each deposit and sum their future values. The formula for the future value of a compound interest account is $A = P(1 + \frac{r}{n})^{nt}$, where $A$ is the amount of money accumulated after n years, including interest, $P$ is the principal amount (initial deposit), $r$ is the annual nominal interest rate (decimal), $n$ is the number of times the interest is compounded per year, and $t$ is the time the money is deposited for in years.1. For the initial $2,500 deposited for 3 years (12 quarters), the future value is:$$A_1 = 2500(1 + \frac{0.04}{4})^{4*3} = 2500(1 + 0.01)^{12} = 2500(1.01)^{12}$$2. For the $5,000 added after 1 year, it will be compounded 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 be compounded 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:- $A_1 = 2500(1.01)^{12} ≈ 2816.89$- $A_2 = 5000(1.01)^{8} ≈ 5412.16$- $A_3 = 7500(1.01)^{4} ≈ 7806.83$Adding them together gives the total amount in the account after 3 years:$$Total = A_1 + A_2 + A_3 ≈ 2816.89 + 5412.16 + 7806.83 = 16035.88$$Therefore, the correct answer is $16,035.88.

Question 9

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 10

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

Using the formula for calculating the payment on an amortized loan:

Payment = (Loan amount * interest rate) / (1 - (1 + interest rate)^-n)

where n = number of payment periods

We can calculate the payment amount to be:

Payment = ($100,000 * 0.085) / (1 - (1 + 0.085)^-10) = $16,447.21

To calculate the amount of interest paid in Year 2, we need to find the remaining balance after the first year's payment has been made.

Using the formula for calculating the remaining balance on an amortized loan after n payment periods:

Remaining balance = (Loan amount * (1 + interest rate)^n) - (Payment * ((1 + interest rate)^n - 1) / interest rate)

After 1 year, the remaining balance is:

Remaining balance = ($100,000 * 1.085^1) - ($16,447.21 * ((1.085^1) - 1) / 0.085) = $84,357.28

To calculate the interest paid in Year 2, we first need to calculate the interest portion of the second payment.

Interest portion of payment = Remaining balance * interest rate

Interest portion of payment = $84,357.28 * 0.085 = $7,174.47

The remaining portion of the payment goes towards reducing the principal balance.

Principal portion of payment = Payment - Interest portion of payment = $16,447.21 - $7,174.47 = $9,272.74

Therefore, the amount of interest paid in Year 2 is the interest portion of the second payment, which is $7,174.47. The closest answer choice is B: $7,927.

Question 11

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

Using present value formula, 
PV = C1/(1+r) + C2/(1+r)^2 + C3/(1+r)^3 + X/(1+r)^4 + X/(1+r)^5 + X/(1+r)^6 + X/(1+r)^7
2500/(1+0.08) + 5000/(1+0.08)^2 + 7500/(1+0.08)^3 + X/(1+0.08)^4 + X/(1+0.08)^5 + X/(1+0.08)^6 + X/(1+0.08)^7 = 25000
X = $4,733.15 (rounded to two decimal places)

Question 12

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

To solve this, we first need to calculate the monthly payment amount and then determine how much of the second payment is applied to the principal. The loan amount is $72,500, the annual nominal interest rate is 11.0%, and since it's compounded monthly, the monthly interest rate is $11.0\% / 12 = 0.9167\%$.1. **Monthly Payment Calculation**: The monthly payment can be calculated using the formula for an installment loan, which is $PMT = P \times \frac{r(1+r)^n}{(1+r)^n - 1}$, where $P$ is the principal amount ($72,500), $r$ is the monthly interest rate (11%/12 = 0.9167%, or 0.009167 as a decimal), and $n$ is the total number of payments (12).$$PMT = 72,500 \times \frac{0.009167(1+0.009167)^{12}}{(1+0.009167)^{12} - 1} = 72,500 \times \frac{0.009167(1.009167)^{12}}{(1.009167)^{12} - 1} = 72,500 \times 0.088993 = 6,452.51$$2. **Interest for the First Month**: The interest for the first month is calculated on the entire principal amount, which is $72,500 \times 0.009167 = 664.63$.3. **Principal Repayment in the First Month**: The principal repayment in the first month is the total monthly payment minus the interest portion, which is $6,452.51 - 664.63 = 5,787.88$.4. **Outstanding Principal After the First Payment**: Subtract the principal repayment from the original loan amount to find the outstanding principal, which is $72,500 - 5,787.88 = 66,712.12$.5. **Interest for the Second Month**: The interest for the second month is calculated on the new principal amount, which is $66,712.12 \times 0.009167 = 611.57$.6. **Principal Repayment in the Second Month**: The principal repayment in the second month is the total monthly payment minus the interest portion for the second month, which is $6,452.51 - 611.57 = 5,840.94$.7. **Percentage of the 2nd Payment Going Toward Principal**: To find the percentage of the second payment that goes toward the principal, divide the principal repayment in the second month by the total monthly payment and multiply by 100.$\frac{5,840.94}{6,452.51} \times 100 = 90.45\%$Therefore, 90.45% of the second monthly payment will go toward the repayment of principal.

Question 13

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 14

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

The answer of Your sister turned 35 today, and she...

Question 15

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 16

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

Accepted Answer

The future value of an annuity formula is used to calculate the number of months needed. With a monthly interest rate of 1.5% (18% annual rate divided by 12 months), and monthly deposits of $5,000, it takes approximately 38 months to reach $250,000.

Question 17

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...

Question 18

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 19

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

First, we need to calculate the annual payment using the amortization formula:
PMT = r * PV / (1 - (1 + r)^(-n))
where
PMT = annual payment
r = annual interest rate
PV = present value of the loan
n = number of payments

Plugging in the given values:
PMT = 0.075 * 35,000 / (1 - (1 + 0.075)^(-7))
PMT = $6,188.01

In the second year, we need to calculate the interest portion of the second payment. To do this, we first need to find the principal portion of the first payment, which we can do using the formula:
Principal = PMT - r * PV
where
Principal = principal portion of the payment
PMT = payment amount
r = annual interest rate
PV = present value of the loan

Plugging in the given values:
Principal = $6,188.01 - 0.075 * $35,000
Principal = $3,758.51

Since the loan is being amortized, the principal portion of each payment will increase and the interest portion will decrease. In the second year, the principal portion will be higher and the interest portion will be lower than in the first year. To find the interest portion of the second payment, we need to subtract the principal portion of the first payment from the total interest paid over the first two payments:

Total interest paid over first two payments = r * PV + r * (PV - Principal)
Total interest paid over first two payments = 0.075 * $35,000 + 0.075 * ($35,000 - $3,758.51)
Total interest paid over first two payments = $5,371.49

Interest portion of second payment = Total interest paid over first two payments - Interest portion of first payment
Interest portion of second payment = $5,371.49 - ($6,188.01 - $3,758.51)
Interest portion of second payment = $2,326.27

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

Quiz 4: Time Value of Money

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?

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?

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?

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 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?

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?

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 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?

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?