Question 1

Sally deposits $10,200 today in a fund earning interest at j₂ = 6%.She wishes to withdraw $600 every 6 months for as long as possible,with the first withdrawal made today.Including the withdrawal made today,how many full withdrawals of $600 would she be able to make?

Accepted Answer

Sally can make 23 full withdrawals of $600. The first withdrawal reduces her initial deposit to $9600. Using the formula for the present value of an annuity (PVA = PMT * [(1 - (1 + r)^-n) / r]), where PMT is the payment amount ($600), r is the semi-annual interest rate (3% or 0.03, since the annual rate is 6%), and n is the number of periods. Solving for n gives us the total number of withdrawals, including the first one.

Question 2

Trish needs to have $20,000 one year from now.She plans to make 9 equal monthly deposits,first deposit made today.What is the size of each deposit needed if the money is deposited into an account paying j₁₂ = 6%?

Accepted Answer

The future value of an annuity is given by the formula:FV = PMT * [(1 + r/n)^(n*t) - 1] / (r/n)where:PMT is the payment amountr is the annual interest raten is the number of compounding periods per yeart is the number of yearsIn this case, we have:FV = $20,000r = 6% = 0.06n = 12 (monthly compounding)t = 1 yearSubstituting these values into the formula, we get:$20,000 = PMT * [(1 + 0.06/12)^(12*1) - 1] / (0.06/12)Solving for PMT, we get:PMT = $2135.12Therefore, the size of each deposit needed is $2135.12.

Question 3

To buy a used car,you have two options.You can pay $10,400 in cash today (December 12,2014)or you can pay $R every month,from December 12,2014 and to July 12,2017.If the interest rate is j₁₂ = 6%,what is R?

Accepted Answer

The answer of To buy a used car,you have two...

Question 4

You can buy a used car for cash of $A on August 12,2010,OR make quarterly payments of $500,starting August 12,2010 and finishing on August 12,2016.If the loan charges interest at j₄ = 4%,what is the value of A?

Accepted Answer

The answer of You can buy a used car for...

Question 5

A $1000 loan is being paid off with annual payments of $100 at the end of each year for as long as necessary,with the final $100 payment increased by a balloon payment.If j₁ = 3.5%,what is the size of the balloon payment?

Accepted Answer

The answer of A $1000 loan is being paid off...

Question 6

You deposit $100 every three months for the next 50 years,first deposit made today.If the interest rate is j₄ = 10%,how much do you have three months after your last deposit?

Accepted Answer

The answer of You deposit $100 every three months for...

Question 7

Deposits of $725 are made into an account earning j₄ = 10% in order to accumulate to $21,500.It turns out that 22 deposits are needed,plus a bit more.If the final deposit is a drop payment made 3 months after the last regular deposit,what is the size of this final deposit?

Accepted Answer

The answer of Deposits of $725 are made into an...

Question 8

A university student wins a scholarship worth $50,000.Instead of the lump sum,she chooses to be paid by 48 monthly payments of $R,with the first monthly payment to be made 5 months from now.If the money earns interest at j₁₂ = 9%,what is the monthly payment?

Accepted Answer

First, we need to calculate the present value of the scholarship, which is:
PV = $50,000 / (1 + 0.09/12)^5 = $38,658.51

Then, we can use the formula for the monthly payment of an annuity:
R = PV / ( (1 - (1+i)^(-n)) / i ), where i = 0.09/12 and n = 48

Substituting the values, we get:
R = $38,658.51 / ( (1 - (1+0.09/12)^(-48)) / (0.09/12) ) ≈ $1282.00

Therefore, the best choice is B, with a monthly payment of $1282.00.

Question 9

Jim buys some furniture for $3850.He pays $200 down and repays the rest with 24 monthly payments of $R,first payment due 3 months from today.If j₁₂ = 9%,what is R?

Accepted Answer

The correct answer is A because the present value of the 24 monthly payments must be equal to the amount of the loan. The present value of the 24 monthly payments is:PV = R * (1 - (1 + j/12)^-24) / (j/12)where j is the annual interest rate and R is the monthly payment.Substituting the given values into the equation, we get:3850 = R * (1 - (1 + 0.09/12)^-24) / (0.09/12)Solving for R, we get:R = $169.26

Question 10

An education fund of $40,000 is to be accumulated by making payments of $400 at the end of every 3-month period,plus a smaller concluding payment.Determine the number of full payments required if j₄ = 9%.

Accepted Answer

We can use the formula for the present value of an annuity to solve this problem:

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

where PV is the present value (in this case, $40,000), PMT is the payment ($400), i is the interest rate per period (9%/4 = 2.25%), and n is the number of periods.

Substituting in the known values, we get:

$40,000 = ($400/0.0225) * (1 - (1/(1.0225)^n))

$40,000 = $17,777.78 * (1 - (1/1.0225)^n)

2.25 = (1/1.0225)^n

log(2.25) = n*log(1.0225)

n = log(2.25)/log(1.0225)

n = 52.65

Since we can't have a fraction of a payment, we round up to the nearest whole number, which gives us 53. However, we need to subtract the smaller concluding payment, so the actual number of full payments required is 52. Therefore, the answer is (C).

Question 11

Mrs.Smith makes 20 annual deposits of $2000 into a retirement savings account,first deposit made today.If she earns j₁ = 5% on her money,how much does she have 25 years from today?

Accepted Answer

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

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

where:

FV = future value
Pmt = payment (in this case, $2000)
r = annual interest rate (in this case, 5%)
n = number of times interest is compounded per year (in this case, once per year)
t = number of years (in this case, 25)

Plugging in the values, we get:

FV = 2000 * (((1 + 0.05/1)^(1*20)) - 1) / (0.05/1)
FV = $88,623.08

Therefore, the best choice is C, with a future value of $88,623.08.

Question 12

Mr.A deposits $5000 today in a fund earning interest at j₂ = 6%.He wishes to withdraw $490 every 6 months for as long as possible.He will make his first withdrawal exactly 2 years from today.When will he make the final smaller concluding (drop)withdrawal?

Accepted Answer

First, we need to calculate the amount Mr. A will have in the fund after 2 years of compounding interest at 6%:

FV = PV x (1 + r)^n
PV = $5000
r = 0.06
n = 2

FV = $5000 x (1 + 0.06)^2
FV = $5,635.20

Now, we need to calculate the amount of each semi-annual withdrawal:

r = 0.06
n = 20 (since there are 20 semi-annual periods in 10 years)
PMT = $490

PV = PMT x ((1 - (1 + r)^-n) / r) 
PV = $490 x ((1 - (1 + 0.06)^-20) / 0.06)
PV = $6,614.50

So Mr. A will be able to withdraw $6,614.50 every 6 months for 10 years. The final withdrawal will be made at the end of the 20th semi-annual period, which is 9 years from now:

Final Withdrawal Date = 2 years + (20 x 6 months) = 2 years + 10 years = 12 years
Final Withdrawal Date = 9 years from now

Question 13

You buy furniture today for $A and "don't pay a cent for 6 months".At the end of 6 months,you begin making monthly payments of $125 for 36 months.If this payment plan charges interest at j₁₂ = 7.2%,what is A?

Accepted Answer

The answer of You buy furniture today for $A and...

Question 14

Sally wants to accumulate $11,500.She makes deposits of $500 at the end of every 6 months in a fund earning interest at j₂ = 5%.It turns out that after making 18 deposits,she is still short of her goal by $306.83.What is the size of the smaller concluding deposit (drop payment)needed 6 months later in order for her to reach (or exceed)her goal of $11,500?

Accepted Answer

The answer of Sally wants to accumulate $11,500.She makes deposits...

Question 15

A loan of $10,000 is to be repaid by 60 monthly payments of $205.00 plus a smaller concluding payment made one month after the last $205 payment.Payments begin one month from now.If j₁₂ = 9%,find the amount of the smaller final payment.

Accepted Answer

The loan repayment can be calculated using the formula for the present value of an annuity plus the present value of a single future payment. The total loan amount is the present value of 60 payments of $205 each, plus the present value of the final smaller payment. Using the given interest rate of 9% per annum, monthly interest rate is 0.75% (9% / 12 months). The present value of the annuity (60 payments of $205) can be calculated using the formula PV = PMT * [(1 - (1 + i)^-n) / i], where PMT is the payment amount, i is the monthly interest rate in decimal form, and n is the total number of payments. The present value of the final payment is calculated using the formula PV = FV / (1 + i)^n, where FV is the future value of the payment, i is the monthly interest rate in decimal form, and n is the number of periods until the payment is made. Subtracting the present value of the annuity from the total loan amount gives the present value of the final payment, which can then be adjusted to find its future value, or the amount of the final payment.

Question 16

To buy some furniture,you can put $150 down and "don't pay a cent" for 6 months.At the end of 6 months,you begin making monthly payments of $100 for 2-years.If j₁₂ = 8.4%,what is the equivalent cash price of the furniture?

Accepted Answer

The equivalent cash price of the furniture is the present value of the future payments. The future payments consist of the down payment of $150, followed by 24 monthly payments of $100 each. The present value of these payments can be calculated using the formula for the present value of an annuity:PV = PMT * [1 - (1 + r)^-n] / rwhere:PV is the present valuePMT is the monthly paymentr is the monthly interest raten is the number of monthsIn this case, the monthly payment is $100, the monthly interest rate is 8.4% / 12 = 0.7%, and the number of months is 24. Plugging these values into the formula, we get:PV = 100 * [1 - (1 + 0.007)^-24] / 0.007= 100 * [1 - 0.75816] / 0.007= 100 * 0.24184 / 0.007= 2276.68Therefore, the equivalent cash price of the furniture is $2276.68.

Question 17

You can buy a car with 60-monthly payments of $350,first payment made today.If j₁₂ = 3%,what is the equivalent cash price of the car,payable today?

Accepted Answer

The equivalent cash price is the present value of the annuity. Using the formula for the present value of an annuity due, where payments are made at the beginning of each period, and given j12 = 3% (monthly interest rate of 0.25%), the calculation results in approximately $19,527.02.

Question 18

A company has developed a unique way to allow their employees to accumulate $5000 in order to buy $5000 worth of shares in the company.The company will set up an account for each employee,paying interest at j₁₂ = 12%.At the end of every month the company will deduct an amount from an employee's pay and deposit it into this account (first deduction made 1 month from now).The company has decided to deduct n-payments of $81.25,plus make a smaller concluding deduction one month after the final deduction of $81.25,at which time the employee will have $5000.What is the size of this smaller concluding deduction?

Accepted Answer

The answer of A company has developed a unique way...

Question 19

To buy a car,you are given two options.Option 1 is to pay $20,000 cash today.Option 2 is to make monthly payments of $500 for as long as necessary,first payment made today.If the dealer charges interest at j₁₂ = 5.4%,how many payments are needed,including the very first one,if the final payment is increased by a balloon payment?

Accepted Answer

Using the present value formula, we can find that the total cost of option 2 with monthly payments is:

PV = (500/0.0045)(1-1/1.0045^Nx12) + 20000/(1.0045^(Nx12))

where Nx12 is the number of monthly payments needed and PV is the present value of all the payments.

To find the number of payments needed with a balloon payment, we can set PV equal to 20000 and solve for Nx12.

20000 = (500/0.0045)(1-1/1.0045^Nx12) + 20000/(1.0045^(Nx12))

Solving this equation using a spreadsheet or calculator, we get Nx12 = 42.95, which means we need 43 payments including the very first one. Therefore, option B is the best choice since it requires fewer overall payments and a lower total cost compared to option 1.

Question 20

Jerry makes semi-annual deposits of $R into a fund paying j₂ = 5%.His first deposit was made on March 15,2011.His last deposit will be made on March 15,2015.On September 15,2015 he has accumulated $15,000 in the fund.What is R?

Accepted Answer

The correct answer is A because the future value of the semi-annual deposits on September 15, 2015 is $15,000. The future value of each deposit is $R * (1 + j2)^n, where j2 is the semi-annual interest rate and n is the number of semi-annual periods. The first deposit was made on March 15, 2011, and the last deposit will be made on March 15, 2015. There are 8 semi-annual periods between March 15, 2011, and September 15, 2015. The future value of the first deposit is $R * (1 + 0.05)^8 = $R * 1.47010. The future value of the last deposit is $R * (1 + 0.05)^0 = $R. The future value of all of the deposits is $R * 1.47010 + $R * 1.47010 + ... + $R * 1.47010 + $R = $R * 1.47010 * 8 = $15,000. Solving for R, we get R = $15,000 / 1.47010 = $1470.10.

Quiz 3: Simple Annuities

Sally deposits $10,200 today in a fund earning interest at j₂ = 6%.She wishes to withdraw $600 every 6 months for as long as possible,with the first withdrawal made today.Including the withdrawal made today,how many full withdrawals of $600 would she be able to make?

Trish needs to have $20,000 one year from now.She plans to make 9 equal monthly deposits,first deposit made today.What is the size of each deposit needed if the money is deposited into an account paying j₁₂ = 6%?

To buy a used car,you have two options.You can pay $10,400 in cash today (December 12,2014) or you can pay $R every month,from December 12,2014 and to July 12,2017.If the interest rate is j₁₂ = 6%,what is R?

You can buy a used car for cash of $A on August 12,2010,OR make quarterly payments of $500,starting August 12,2010 and finishing on August 12,2016.If the loan charges interest at j₄ = 4%,what is the value of A?

A $1000 loan is being paid off with annual payments of $100 at the end of each year for as long as necessary,with the final $100 payment increased by a balloon payment.If j₁ = 3.5%,what is the size of the balloon payment?

You deposit $100 every three months for the next 50 years,first deposit made today.If the interest rate is j₄ = 10%,how much do you have three months after your last deposit?

Deposits of $725 are made into an account earning j₄ = 10% in order to accumulate to $21,500.It turns out that 22 deposits are needed,plus a bit more.If the final deposit is a drop payment made 3 months after the last regular deposit,what is the size of this final deposit?

A university student wins a scholarship worth $50,000.Instead of the lump sum,she chooses to be paid by 48 monthly payments of $R,with the first monthly payment to be made 5 months from now.If the money earns interest at j₁₂ = 9%,what is the monthly payment?

Jim buys some furniture for $3850.He pays $200 down and repays the rest with 24 monthly payments of $R,first payment due 3 months from today.If j₁₂ = 9%,what is R?

An education fund of $40,000 is to be accumulated by making payments of $400 at the end of every 3-month period,plus a smaller concluding payment.Determine the number of full payments required if j₄ = 9%.

Mrs.Smith makes 20 annual deposits of $2000 into a retirement savings account,first deposit made today.If she earns j₁ = 5% on her money,how much does she have 25 years from today?

Mr.A deposits $5000 today in a fund earning interest at j₂ = 6%.He wishes to withdraw $490 every 6 months for as long as possible.He will make his first withdrawal exactly 2 years from today.When will he make the final smaller concluding (drop) withdrawal?

You buy furniture today for $A and "don't pay a cent for 6 months".At the end of 6 months,you begin making monthly payments of $125 for 36 months.If this payment plan charges interest at j₁₂ = 7.2%,what is A?

A loan of $10,000 is to be repaid by 60 monthly payments of $205.00 plus a smaller concluding payment made one month after the last $205 payment.Payments begin one month from now.If j₁₂ = 9%,find the amount of the smaller final payment.

To buy some furniture,you can put $150 down and "don't pay a cent" for 6 months.At the end of 6 months,you begin making monthly payments of $100 for 2-years.If j₁₂ = 8.4%,what is the equivalent cash price of the furniture?

You can buy a car with 60-monthly payments of $350,first payment made today.If j₁₂ = 3%,what is the equivalent cash price of the car,payable today?

Jerry makes semi-annual deposits of $R into a fund paying j₂ = 5%.His first deposit was made on March 15,2011.His last deposit will be made on March 15,2015.On September 15,2015 he has accumulated $15,000 in the fund.What is R?

Quiz 3: Simple Annuities

Sally deposits $10,200 today in a fund earning interest at j2 = 6%.She wishes to withdraw $600 every 6 months for as long as possible,with the first withdrawal made today.Including the withdrawal made today,how many full withdrawals of $600 would she be able to make?

Trish needs to have $20,000 one year from now.She plans to make 9 equal monthly deposits,first deposit made today.What is the size of each deposit needed if the money is deposited into an account paying j12 = 6%?

To buy a used car,you have two options.You can pay $10,400 in cash today (December 12,2014) or you can pay $R every month,from December 12,2014 and to July 12,2017.If the interest rate is j12 = 6%,what is R?

You can buy a used car for cash of $A on August 12,2010,OR make quarterly payments of $500,starting August 12,2010 and finishing on August 12,2016.If the loan charges interest at j4 = 4%,what is the value of A?

A $1000 loan is being paid off with annual payments of $100 at the end of each year for as long as necessary,with the final $100 payment increased by a balloon payment.If j1 = 3.5%,what is the size of the balloon payment?

You deposit $100 every three months for the next 50 years,first deposit made today.If the interest rate is j4 = 10%,how much do you have three months after your last deposit?

Deposits of $725 are made into an account earning j4 = 10% in order to accumulate to $21,500.It turns out that 22 deposits are needed,plus a bit more.If the final deposit is a drop payment made 3 months after the last regular deposit,what is the size of this final deposit?

A university student wins a scholarship worth $50,000.Instead of the lump sum,she chooses to be paid by 48 monthly payments of $R,with the first monthly payment to be made 5 months from now.If the money earns interest at j12 = 9%,what is the monthly payment?

Jim buys some furniture for $3850.He pays $200 down and repays the rest with 24 monthly payments of $R,first payment due 3 months from today.If j12 = 9%,what is R?

An education fund of $40,000 is to be accumulated by making payments of $400 at the end of every 3-month period,plus a smaller concluding payment.Determine the number of full payments required if j4 = 9%.

Mrs.Smith makes 20 annual deposits of $2000 into a retirement savings account,first deposit made today.If she earns j1 = 5% on her money,how much does she have 25 years from today?

Mr.A deposits $5000 today in a fund earning interest at j2 = 6%.He wishes to withdraw $490 every 6 months for as long as possible.He will make his first withdrawal exactly 2 years from today.When will he make the final smaller concluding (drop) withdrawal?

You buy furniture today for $A and "don't pay a cent for 6 months".At the end of 6 months,you begin making monthly payments of $125 for 36 months.If this payment plan charges interest at j12 = 7.2%,what is A?

A loan of $10,000 is to be repaid by 60 monthly payments of $205.00 plus a smaller concluding payment made one month after the last $205 payment.Payments begin one month from now.If j12 = 9%,find the amount of the smaller final payment.

To buy some furniture,you can put $150 down and "don't pay a cent" for 6 months.At the end of 6 months,you begin making monthly payments of $100 for 2-years.If j12 = 8.4%,what is the equivalent cash price of the furniture?

You can buy a car with 60-monthly payments of $350,first payment made today.If j12 = 3%,what is the equivalent cash price of the car,payable today?

Jerry makes semi-annual deposits of $R into a fund paying j2 = 5%.His first deposit was made on March 15,2011.His last deposit will be made on March 15,2015.On September 15,2015 he has accumulated $15,000 in the fund.What is R?

Sally deposits $10,200 today in a fund earning interest at j₂ = 6%.She wishes to withdraw $600 every 6 months for as long as possible,with the first withdrawal made today.Including the withdrawal made today,how many full withdrawals of $600 would she be able to make?

Trish needs to have $20,000 one year from now.She plans to make 9 equal monthly deposits,first deposit made today.What is the size of each deposit needed if the money is deposited into an account paying j₁₂ = 6%?

To buy a used car,you have two options.You can pay $10,400 in cash today (December 12,2014) or you can pay $R every month,from December 12,2014 and to July 12,2017.If the interest rate is j₁₂ = 6%,what is R?

You can buy a used car for cash of $A on August 12,2010,OR make quarterly payments of $500,starting August 12,2010 and finishing on August 12,2016.If the loan charges interest at j₄ = 4%,what is the value of A?

A $1000 loan is being paid off with annual payments of $100 at the end of each year for as long as necessary,with the final $100 payment increased by a balloon payment.If j₁ = 3.5%,what is the size of the balloon payment?

You deposit $100 every three months for the next 50 years,first deposit made today.If the interest rate is j₄ = 10%,how much do you have three months after your last deposit?

Deposits of $725 are made into an account earning j₄ = 10% in order to accumulate to $21,500.It turns out that 22 deposits are needed,plus a bit more.If the final deposit is a drop payment made 3 months after the last regular deposit,what is the size of this final deposit?

A university student wins a scholarship worth $50,000.Instead of the lump sum,she chooses to be paid by 48 monthly payments of $R,with the first monthly payment to be made 5 months from now.If the money earns interest at j₁₂ = 9%,what is the monthly payment?

Jim buys some furniture for $3850.He pays $200 down and repays the rest with 24 monthly payments of $R,first payment due 3 months from today.If j₁₂ = 9%,what is R?

An education fund of $40,000 is to be accumulated by making payments of $400 at the end of every 3-month period,plus a smaller concluding payment.Determine the number of full payments required if j₄ = 9%.

Mrs.Smith makes 20 annual deposits of $2000 into a retirement savings account,first deposit made today.If she earns j₁ = 5% on her money,how much does she have 25 years from today?

Mr.A deposits $5000 today in a fund earning interest at j₂ = 6%.He wishes to withdraw $490 every 6 months for as long as possible.He will make his first withdrawal exactly 2 years from today.When will he make the final smaller concluding (drop) withdrawal?

You buy furniture today for $A and "don't pay a cent for 6 months".At the end of 6 months,you begin making monthly payments of $125 for 36 months.If this payment plan charges interest at j₁₂ = 7.2%,what is A?

A loan of $10,000 is to be repaid by 60 monthly payments of $205.00 plus a smaller concluding payment made one month after the last $205 payment.Payments begin one month from now.If j₁₂ = 9%,find the amount of the smaller final payment.

To buy some furniture,you can put $150 down and "don't pay a cent" for 6 months.At the end of 6 months,you begin making monthly payments of $100 for 2-years.If j₁₂ = 8.4%,what is the equivalent cash price of the furniture?

You can buy a car with 60-monthly payments of $350,first payment made today.If j₁₂ = 3%,what is the equivalent cash price of the car,payable today?

Jerry makes semi-annual deposits of $R into a fund paying j₂ = 5%.His first deposit was made on March 15,2011.His last deposit will be made on March 15,2015.On September 15,2015 he has accumulated $15,000 in the fund.What is R?