Question 1

Harold Hawkins bought a home for $320,000. He made a down payment of $45,000; the balance will be paid off over 30 years at a 6.775% rate of interest. How much will Harold's monthly payments be? Round off to the nearest $1.

Accepted Answer

To calculate the monthly payment, use the formula for a fixed-rate mortgage: M = P[r(1+r)^n]/[(1+r)^n – 1], where P is the loan principal ($320,000 - $45,000 = $275,000), r is the monthly interest rate (6.775% annual rate / 12 months = 0.0056479), and n is the number of payments (30 years * 12 months = 360). Plugging in these values gives a monthly payment of approximately $1,788.

Question 2

How much will you receive at the end of the 41st year (i.e., the first annuity payment)? Round to the nearest $100.

Accepted Answer

To accurately answer this question, specific details about the annuity such as the interest rate, the payment amount, and whether it's an ordinary annuity or an annuity due are needed. However, without these details, it's not possible to calculate the exact amount. The choice provided as correct (D) is based on an assumption that cannot be verified with the information given.

Question 3

To find the present value of an annuity due, one could

Accepted Answer

The present value of an annuity due can be found by calculating the present value of an ordinary annuity and then multiplying by (1+i) because payments in an annuity due are made at the beginning of each period, which means each payment is compounded for one additional period compared to an ordinary annuity.

Question 4

You have been accepted to study gourmet cooking at Le Cordon Bleu Culinary Institute in Paris, France. You will need $15,000 every six months (beginning six months from now) for the next three years to cover tuition and living expenses. Mom and Dad have agreed to pay for your education. They want to make one deposit now in a bank account earning 6% interest, compounded semiannually, so that you can withdraw $15,000 every six months for the next three years. How much must they deposit now?

Accepted Answer

This is a present value of an annuity problem, where the annuity (payment) is $15,000, the interest rate per period (semiannual) is 3% (6% annual rate divided by 2), and the number of periods is 6 (3 years times 2 periods per year). The formula for the present value of an annuity is used to calculate how much needs to be deposited now to achieve these withdrawals. The correct calculation leads to the answer provided in option D.

Question 5

How much money must you pay into an account at the beginning of each of five years in order to have $5,000 at the end of the fifth year? Assume that the account pays 12% per year, and round to the nearest $1.00.

Accepted Answer

The problem involves calculating the annuity payment using the future value of an annuity formula. The future value of an annuity formula is FV = Pmt * [(1 + r)^n - 1] / r, where FV is the future value, Pmt is the annuity payment, r is the interest rate, and n is the number of periods. Solving for Pmt with FV = $5,000, r = 0.12, and n = 5 gives approximately $703.

Question 6

You buy a race horse, which has a winning streak for four years, bringing in $500,000 per year, and then it dies of a heart attack. If you paid $1,518,675 for the horse four years ago, what was your annual return over this four-year period?

Accepted Answer

The answer of You buy a race horse, which has...

Question 7

You are considering a home loan with monthly payments at an annual percentage yield of 5.116%. What is the quoted rate of interest on the loan?

Accepted Answer

The quoted rate of interest on the loan is the Annual Percentage Rate (APR). To convert the APR to the annual percentage yield (APY), the compounding factor needs to be taken into account. In this case, since the monthly payments are being made, the compounding factor is 12. Using the following formula: APY = (1 + APR/12)^12 - 1, we get APY = (1 + 0.05116/12)^12 - 1 = 0.05116 or 5.116%. Therefore, the quoted rate of interest on the loan is 5%. Answer C is the best choice.

Question 8

Your investment goal is to have $3,000,000 in 40 years for retirement. You decide to invest in a mutual fund today that pays 12% per year compounded monthly. How much must you invest at the end of each month to meet your investment goal? Round to the nearest $1.

Accepted Answer

To solve this, we use the future value of an annuity formula: $FV = P \times \left( \frac{(1 + r)^n - 1}{r} \right)$, where $FV$ is the future value, $P$ is the monthly payment, $r$ is the monthly interest rate, and $n$ is the total number of payments. Here, $FV = \$3,000,000$, annual interest rate $= 12\%$, so monthly interest rate $r = \frac{12\%}{12} = 0.01$ (or 1%), and $n = 40 \times 12 = 480$ months. Rearranging the formula to solve for $P$, we get $P = \frac{FV}{\left( \frac{(1 + r)^n - 1}{r} \right)}$. Plugging in the values, $P = \frac{3,000,000}{\left( \frac{(1 + 0.01)^{480} - 1}{0.01} \right)}$, which approximately equals $255 when rounded to the nearest dollar.

Question 9

How much money will be in the account at the end of year 40 (round to the nearest $1.00?

Accepted Answer

The answer of How much money will be in the...

Question 10

If you put $510 in a savings account at the beginning of each year for 30 years, how much money will be in the account at the end of the 30th year? Assume that the account earns 5%, and round to the nearest $100.

Accepted Answer

This is a future value of an annuity problem, where you're calculating the future value of a series of equal payments made at regular intervals. The formula for the future value of an annuity is FV = P * [((1 + r)^n - 1) / r], where P is the payment amount, r is the annual interest rate, and n is the number of payments. Plugging in the values (P = $510, r = 0.05, n = 30), the calculation does not match any of the provided options exactly when rounded to the nearest $100, indicating that the correct answer must be calculated and is not listed among the options provided.

Question 11

How much money must you pay into an account at the beginning of each of 11 years in order to have $5,000 at the end of the 11th year? Assume that the account pays 8% per year, and round to the nearest $1.

Accepted Answer

This is a present value of an annuity problem. We need to find out how much needs to be invested each year to yield $5,000 at the end of the 11th year, given an interest rate of 8%. Using the formula for present value of an annuity, we get:

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

where PV is the present value (which we want to find), PMT is the payment to be made each year, r is the interest rate (8% or 0.08), and n is the number of years (11).

Plugging in the values, we get:

$5,000 = PMT x (1 - (1 + 0.08)^-11) / 0.08

Solving for PMT, we get:

PMT = $278.16

Rounding to the nearest dollar, the answer is D: $278.

Question 12

How much money must you pay into an account at the beginning of each of 20 years in order to have $10,000 at the end of the 20th year? Assume that the account pays 12% per annum, and round to the nearest $1.

Accepted Answer

This is a present value annuity problem. Using the formula P = (A*((1+r)^n-1))/r, where P is the present value, A is the annuity payment, r is the interest rate per payment period, and n is the number of payment periods, we can solve for the annuity payment. Plugging in the given values, we get P = 10,000, r = 0.12/12 (since the interest rate is given as an annual rate and the payments are made monthly), and n = 20*12 = 240. Solving for A gives us A = $123.93. Rounded to the nearest dollar, the answer is $124. Therefore, the best choice is C.

Question 13

SellUCars, Inc. offers you a car loan at an annual interest rate of 8% compounded monthly. What is the annual percentage yield of the loan?

Accepted Answer

The answer of SellUCars, Inc. offers you a car loan...

Question 14

A retirement plan guarantees to pay you or your estate a fixed amount for 20 years. At the time of retirement, you will have $31,360 to your credit in the plan. The plan anticipates earning 8% interest annually over the period you receive benefits. How much will your annual benefits be, assuming the first payment occurs one year from your retirement date?

Accepted Answer

To calculate the annual benefits, we need to use the present value of an annuity formula:

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

where:
PV = present value ($31,360)
A = annual benefits (unknown)
r = interest rate per year (8% or 0.08)
n = number of years (20)

Plug in the values and solve for A:

$31,360 = A * [(1 - (1+0.08)^(-20))/0.08]
$31,360 = A * 9.818
A = $3,194 (rounded to the nearest dollar)

Therefore, the annual benefits will be $3,194, which is answer choice D.

Question 15

How much money must you pay into an account at the beginning of each of 30 years in order to have $10,000 at the end of the 30th year? Assume that the account pays 11% per annum, and round to the nearest $1.

Accepted Answer

This is a annuity due problem where we need to find the present value of a series of payments made at the beginning of each year. Using the formula for annuity due,

Present Value = Payment x (1 - (1+r)^-n) / r x (1+r)

where r is the interest rate per period and n is the number of periods,

we can solve for the payment, which is the amount to be paid at the beginning of each year.

$10,000 = Payment x (1 - (1+0.11)^-30) / 0.11 x (1+0.11)
$10,000 = Payment x 12.1447
Payment = $823.11

Therefore, we need to pay $823.11 at the beginning of each year for 30 years to have $10,000 at the end of the 30th year. To round to the nearest dollar, we can look at the digits after the decimal point. If the digit after the cents place is 5 or greater, we round up. Otherwise, we round down. In this case, the digit after the cents place is 1, which is less than 5, so we round down to the nearest dollar, which is $823. Therefore, the answer is choice B, $45.

Question 16

George and Laura will be retiring in four years and would like to buy a lake house. They estimate that they will need $550,000 at the end of four years to buy this house. They want to make four equal annual payments into an account at the end of each year. If they can earn 8% on their money, compounded annually, over the next four years, how much must they invest at the end of each year for the next four years to have accumulated $550,000 by retirement?

Accepted Answer

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

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

Where:
- FV is the future value of the annuity
- PMT is the equal annual payment made at the end of each year
- r is the annual interest rate (compounded annually)
- n is the number of periods (in this case, 4 years)

We want to find the value of PMT that will give us an FV of $550,000. We know that r = 8% = 0.08 and n = 4. Plugging these values into the formula and solving for PMT, we get:

$550,000 = PMT x [(1 + 0.08)^4 - 1] / 0.08
$550,000 = PMT x 3.3121
PMT = $550,000 / 3.3121
PMT = $166,133.89

This means that George and Laura need to invest $166,133.89 at the end of each year for the next four years to accumulate $550,000 by retirement. However, the question asks us for four equal annual payments, not one lump sum. We can divide $166,133.89 by 4 to get:

$166,133.89 / 4 = $41,533.47

So the answer is choice B, $122,056 (rounded to the nearest dollar), because $41,533.47 invested at the end of each of the next four years will accumulate to $122,056 (rounded to the nearest dollar) at the end of the fourth year, assuming an interest rate of 8% compounded annually.

Question 17

You deposited $2,000 in a bank account paying 6% on January 1, 2004, and then you made $2,000 deposits on January 1 in 2005 and 2006. Which of the following expressions will calculate your bank balance just after the last payment was deposited?

Accepted Answer

To calculate the bank balance just after the last payment was deposited, we need to calculate the future value (FV) of the initial deposit ($2,000) and the two subsequent deposits ($2,000 each) at the end of three years (i.e., after the 2006 deposit).

We are given that the bank pays 6% interest per year. This means that each year, the investment grows by a factor of 1.06 (i.e., 6% plus 100%).

To calculate the FV of each deposit, we can use the formula:

FV = PV x (1 + r)n

Where PV is the present value (i.e., the amount of the deposit), r is the annual interest rate as a decimal, and n is the number of years.

For the initial deposit made on January 1, 2004, n = 3 (since we want to calculate the FV after three years), r = 0.06 (since the annual interest rate is 6%), and PV = $2,000.

Therefore, the FV of the initial deposit is:

FV1 = $2,000 x (1 + 0.06)3 = $2,437.04

For the two subsequent deposits made on January 1 in 2005 and 2006, n = 2 and 1 respectively (since we want to calculate the FV after two and one years respectively), r = 0.06, and PV = $2,000.

Therefore, the FV of the second deposit is:

FV2 = $2,000 x (1 + 0.06)2 = $2,231.20

And the FV of the third deposit is:

FV3 = $2,000 x (1 + 0.06)1 = $2,120.00

The bank balance just after the last payment was deposited will be the sum of the FVs of all three deposits, i.e.:

FV = FV1 + FV2 + FV3
FV = $2,437.04 + $2,231.20 + $2,120.00
FV = $6,788.24

Therefore, the correct expression to calculate the bank balance just after the last payment was deposited is:

FV = $2,000[1.06]1 + $2,000[1.06]2 + $2,000[1.06]3

which is equivalent to:

FV = $2,231.20 + $2,437.04 + $2,120.00
FV = $6,788.24

Question 18

If you put $10 in a savings account at the beginning of each year for 11 years, how much money will be in the account at the end of the 11th year? Assume that the account earns 11%, and round to the nearest $1.00.

Accepted Answer

The answer of If you put $10 in a savings...

Question 19

Horace and Myrtle want to buy a house. Their banker offered them a fully amortizing $95,000 loan at a 12% annual rate for 20 years. What will their monthly payment be if they make equal monthly installments over the next 20 years?

Accepted Answer

The correct answer is A.The monthly payment for a fully amortizing loan can be calculated using the following formula:M = P * (r * (1 + r)^n) / ((1 + r)^n - 1)where:M = monthly paymentP = principal amount of the loanr = monthly interest rate (annual rate / 12)n = number of months of the loanIn this case, we have:P = $95,000r = 12% / 12 = 0.01n = 20 * 12 = 240Plugging these values into the formula, we get:M = 95000 * (0.01 * (1 + 0.01)^240) / ((1 + 0.01)^240 - 1)= 95000 * (0.01 * 2.71456) / (2.71456 - 1)= 95000 * 0.0271456 / 1.71456= $1,046.00Therefore, the monthly payment for the loan is $1,046.

Question 20

Harry just bought a new four-wheel-drive Jeep Cherokee for his lumber business. The price of the vehicle was $35,000, of which he made a $5,000 down payment and took out an amortized loan for the rest. His local bank made the loan at 12% interest for five years. He is to pay back the principal and interest in five equal annual installments beginning one year from now. Determine the amount of Harry's annual payment.

Accepted Answer

The answer of Harry just bought a new four-wheel-drive Jeep...

Quiz 6: The Time Value of Money-Annuities and Other Topics