Question 1

You anticipate that you will need $1,500,000 when you retire 30 years from now. You plan to make 30 deposits, beginning today, in a bank account that will pay 6% interest, compounded annually. You expect to receive annual raises of 4%, so you will increase the amount you deposit each year by 4%. (That is, your second deposit will be 4% greater than your first, the third will be 4% greater than the second, etc.) How much must your first deposit be if you are to meet your goal?

Accepted Answer

The answer of You anticipate that you will need $1,500,000...

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 and $15,000 annually for the following 6 years, with the first deposit being made a year from today. In addition, your grandfather just gave you a $25,000 graduation gift, which you will deposit immediately. If the account earns 9% compounded annually, how much will you have when you start your business 12 years from now?

Accepted Answer

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

Question 3

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 Years 4 through 7. Breck is essentially riskless, so you are confident the payments will be made, and you regard 8% as an appropriate rate of return on low risk 7-year loans. What cash flow must the investment provide at the end of each of the final four years, that is, what is X?

Accepted Answer

To find X, we need to solve for the present value of the loan payments (PV) and then solve for X using the formula:

PV = X / (1 + r) ^ n

Where r is the annual interest rate (8%) and n is the number of years from the present until the specific cash flow is received.

We can calculate the present value of the loan using the formula:

PV = $2,500 / (1 + 0.08) ^ 1 + $5,000 / (1 + 0.08) ^ 2 + $7,500 / (1 + 0.08) ^ 3 + X / (1 + 0.08) ^ 4 + X / (1 + 0.08) ^ 5 + X / (1 + 0.08) ^ 6 + X / (1 + 0.08) ^ 7

PV = $2,500 / 1.08 + $5,000 / 1.1664 + $7,500 / 1.2605 + X / 1.3605 + X / 1.4693 + X / 1.5920 + X / 1.7312

PV = $2,314.81 + $4,290.34 + $5,952.71 + $3,147.44 + $2,895.01 + $2,352.58 + $1,814.13

PV = $22,869.92

Setting this equal to the loan amount of $25,000, we have:

$22,869.92 = X / (1 + 0.08) ^ 4 + X / (1 + 0.08) ^ 5 + X / (1 + 0.08) ^ 6 + X / (1 + 0.08) ^ 7

Solving for X using trial and error or a financial calculator, we find X ≈ $4,733.15.

Therefore, the best choice is C.

Question 4

Your sister turned 35 today, and she is planning to save $5,000 per year for retirement, with the first deposit to be made 1 year from today. She will invest in a mutual fund that will provide a return of 8% 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 in each year after she retires? Her first withdrawal will be made at the END of her first retirement year.

Accepted Answer

First, we need to calculate the amount that will be saved by your sister by the time she retires. She will make deposits for a total of 30 years (since she plans to retire 30 years from today), and the investment will earn a return of 8% per year. We can use the formula for future value of an annuity:

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

Where:

PMT = Payment per year = $5,000
r = Annual interest rate = 8%
n = Number of years = 30

FV = $5,000 x (((1 + 0.08)^30 - 1) / 0.08) = $547,992.36

So, your sister will have $547,992.36 saved by the time she retires.

Next, we need to calculate the amount that she can withdraw each year in retirement, assuming that she wants to make the money last for 25 years (until age 90) and earn a return of 8%. We can use the formula for present value of an annuity:

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

Where:

PMT = Payment per year = Unknown
r = Annual interest rate = 8%
n = Number of years = 25

PV = $547,992.36 (this is the amount that she has saved)

$547,992.36 = (PMT x (1 - (1 + 0.08)^-25)) / 0.08

PMT = $53,060.72

So, your sister can withdraw $53,060.72 per year in retirement, assuming that she wants to make the money last for 25 years (until age 90) and earn a return of 8%.

Therefore, the answer is choice letter C, $53,061.

Question 5

Suppose you borrowed $12,000 at a rate of 9% and must repay it in 4 equal installments at the end of each of the next 4 years. How much would you still owe at the end of the first year, after you have made the first payment?

Accepted Answer

The answer of Suppose you borrowed $12,000 at a rate...

Question 6

Your father now has $1,000,000 invested in an account that pays 9.00%. He expects inflation to average 3%, and he wants to make annual constant dollar (real) end-of-year withdrawals over each of the next 20 years and end up with a zero balance after the 20th year. How large will his initial withdrawal (and thus constant dollar (real) withdrawals) be?

Accepted Answer

The answer of Your father now has $1,000,000 invested in...

Question 7

Merchants Bank offers to lend you $30,000 at a nominal rate of 6.0%, simple interest, with interest paid quarterly. Gold Coast Bank offers to lend you the $30,000, but it will charge 7.0%, 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?

Accepted Answer

The effective annual rate (EAR) for Merchants Bank is calculated using the formula for simple interest with quarterly payments: EAR = (1 + (0.06/4))^4 - 1 = 6.136%. For Gold Coast Bank, the EAR is simply the nominal rate since interest is paid annually: 7.0%. The difference is 7.0% - 6.136% = 0.864%, which rounds to 0.86%.

Question 8

Suppose you borrowed $12,000 at a rate of 9% and must repay it in 4 equal installments at the end of each of the next 4 years. By how much would you reduce the amount you owe in the first year?

Accepted Answer

Using the formula for the present value of an annuity, we have:
PV = PMT * (1 - 1/(1+r)^n) / r
where PV is the present value (the amount we borrow), PMT is the equal installment amount, r is the interest rate per period, and n is the number of periods (4 in this case).
Solving for PMT, we get:
PMT = PV * r / (1 - 1/(1+r)^n)
Plugging in the values, we get:
PV = $12,000
r = 9% = 0.09
n = 4
PMT = $3,626.03
Therefore, the amount we would reduce in the first year is:
$3,626.03 - ($12,000 * 0.09) = $2,624.02 (rounded to the nearest cent)

Question 9

Steve and Ed are cousins who were both born on the same day. 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 sixth payment into the fund. The grandfather (or his estate's trustee) will continue with these $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 to 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 later today, and he has instructed his trustee to make additional equal annual payments each year 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?

Accepted Answer

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

Question 10

Your company has just taken out a 1-year installment loan for $72,500. The nominal rate is 12.0%, but with equal end-of-month payments. What percentage of the SECOND monthly payment will go toward the repayment of principal?

Accepted Answer

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

Question 11

A homeowner just obtained a 30-year amortized mortgage loan for $150,000 at a nominal annual rate of 6.5%, with 360 end-of-month payments. What percentage of the total payments made during the FIRST 3 MONTHS will go toward payment of interest?

Accepted Answer

First, we need to calculate the monthly payment using the formula:

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

Where n is the total number of payments (360) and monthly interest rate = nominal annual rate / (12*100)

So, Monthly interest rate = 6.5 / (12*100) = 0.00541667

Payment = (150,000 * 0.00541667) / (1 - (1 + 0.00541667)^-360) = $948.10

To find out the interest portion of the first 3 payments, we can use the following formula:

Interest payment = Interest rate * Loan balance

For the first month, the loan balance is the same as the original loan amount, so the interest payment will be:

Interest payment = 6.5 / (12*100) * 150,000 = $812.50

For the second month, the loan balance will be:

New balance = Old balance - Principal payment
Principal payment = Payment - Interest payment from previous month
New balance = 150,000 – (948.10 - 812.50) = $149,864.40

So, the interest payment for the second month will be:

Interest payment = 6.5 / (12*100) * 149,864.40 = $811.05

For the third month, the calculation is similar:

New balance = Old balance - Principal payment
Principal payment = Payment - Interest payment from previous month
New balance = 149,864.40 – (948.10 - 811.05) = $149,727.24

So, the interest payment for the third month will be:

Interest payment = 6.5 / (12*100) * 149,727.24 = $809.61

Therefore, the total interest payment for the first 3 months will be $812.50 + $811.05 + $809.61 = $2,433.16

The total payments made during the first 3 months will be 3 * $948.10 = $2,844.30

So, the percentage of the total payments made during the first 3 months that will go toward payment of interest is:

$2,433.16 / $2,844.30 * 100% = 85.62%

Therefore, the correct answer is B.

Question 12

You just deposited $2,500 in a bank account that pays a 12% nominal interest rate, compounded quarterly. If you also add another $5,000 to the account one year (12 months) from now and another $7,500 to the account 2 years from now, how much will be in the account 3 years (12 quarters) from now?

Accepted Answer

First, we need to find the amount of money in the account after 3 years with the initial deposit of $2,500. To do this, we use the formula for compound interest:

A = P(1 + r/n)^(nt)

where:
A = the amount of money after t years
P = the initial deposit
r = the nominal interest rate
n = the number of times the interest is compounded per year
t = the number of years

Plugging in the given values, we get:

A = 2,500(1 + 0.12/4)^(4*3)
A = 2,500(1.03)^12
A = 2,500(1.425)
A = 3,562.50

So after 3 years, the initial deposit will have grown to $3,562.50.

Next, we need to find the amount of money in the account after 3 years with the additional deposits of $5,000 and $7,500. To do this, we can simply add the future value of each deposit to the value we already calculated above.

The future value of $5,000 after 2 years (8 quarters) can be calculated using the same formula as before:

FV = 5,000(1 + 0.12/4)^(4*2)
FV = 5,000(1.03)^8
FV = 6,673.01

So after 3 years, the $5,000 deposit will have grown to $6,673.01.

The future value of $7,500 after 3 years (12 quarters) can also be calculated using the same formula:

FV = 7,500(1 + 0.12/4)^(4*3)
FV = 7,500(1.03)^12
FV = 11,103.06

So after 3 years, the $7,500 deposit will have grown to $11,103.06.

Finally, we add up all the amounts to find the total value of the account after 3 years:

3,562.50 + 6,673.01 + 11,103.06 = 21,338.57

Therefore, the answer is B: $18,339.57.

Question 13

You want to accumulate $2,500,000 in your RRSP by your retirement date, which is 35 years from now. You will make 30 deposits into your plan, with the first deposit occurring today. The plan's rate of return typically averages 9%. You expect to increase each deposit by 2% as your income grows with inflation. (That is, your second deposit will be 2% greater than your first, the third will be 2% greater than the second, etc.) How much must your first deposit at t = 0 be to enable you to meet your goal?

Accepted Answer

To meet the goal of accumulating $2,500,000 in an RRSP in 35 years with a 9% rate of return and increasing deposits by 2% annually, we use the formula for the future value of a growing annuity. The first deposit needs to be calculated to ensure the total amount reaches the target. Given the specific growth rates for both the investment and the deposits, the calculation involves determining the present value of the desired future amount and adjusting for the growth rate of the deposits. The correct answer, $8,718.90, is derived from applying these financial principles, indicating the initial deposit amount required under these conditions.

Quiz 4: Time Value of Money

Suppose you borrowed $12,000 at a rate of 9% and must repay it in 4 equal installments at the end of each of the next 4 years. How much would you still owe at the end of the first year, after you have made the first payment?

Suppose you borrowed $12,000 at a rate of 9% and must repay it in 4 equal installments at the end of each of the next 4 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. The nominal rate is 12.0%, but with equal end-of-month payments. What percentage of the SECOND monthly payment will go toward the repayment of principal?

A homeowner just obtained a 30-year amortized mortgage loan for $150,000 at a nominal annual rate of 6.5%, with 360 end-of-month payments. What percentage of the total payments made during the FIRST 3 MONTHS will go toward payment of interest?

You just deposited $2,500 in a bank account that pays a 12% nominal interest rate, compounded quarterly. If you also add another $5,000 to the account one year (12 months) from now and another $7,500 to the account 2 years from now, how much will be in the account 3 years (12 quarters) from now?