Question 1

Jennifer already has $15,500 saved for a down payment for a house and she plans to save another $400 at the end of each month for the next three years. If she earns 8.4% compounded monthly how large will her down payment be in three years?
A) $36,123
B) $36,237
C) $37,680
D) $19,924
E) $16,312

Accepted Answer

The total amount saved can be calculated using the future value of a series formula for the monthly savings and adding it to the compounded amount of the initial savings. The future value of the monthly savings (PMT) is calculated using the formula: FV = PMT * [((1 + r)^n - 1) / r], where PMT = $400, r = 0.084/12 (monthly interest rate), and n = 3*12 (number of months). The future value of the initial savings is calculated using the compound interest formula: FV = P(1 + r)^n, where P = $15,500, r = 0.084/12, and n = 3*12. Adding both values gives the total amount saved, which matches option B, $36,237.

Question 2

How much money would you have at the end of 10 years if you made deposits of $4,000 at the end of every three months into an investment that accumulated at 9% compounded quarterly?
A) $60,772
B) $168,781
C) $255,145
D) $1,351,530
E) $667,273

Accepted Answer

C

Question 3

How much money would you have at the end of five years if you made deposits of $450 at the end of every month into an investment that accumulated at 18% compounded monthly?
A) $116,843
B) $43,297
C) $31,860
D) $27,000
E) $17,721

Accepted Answer

B

Question 4

Sam will contribute $200 to his RRSP at the end of each month for 15 years and then raise his monthly contribution to $500 at the end of each month for the subsequent 20 years. If his investments earn 11.7% compounded monthly, what will be the value of the investments after the last $500 contribution is made 35 years from now?
A) $1,186,877
B) $572,207
C) $1,471,930
D) $521,751
E) $285,054

Accepted Answer

The value of Sam's investments after 35 years can be calculated using the future value of a series formula for annuities, considering the change in monthly contributions after 15 years. For the first 15 years, with a monthly contribution of $200 and an annual interest rate of 11.7% compounded monthly, the future value can be calculated. Then, for the next 20 years, with a monthly contribution of $500 and the same interest rate, the future value of this series is calculated, adding the accumulated value from the first period. The correct calculation leads to a total future value of approximately $1,471,930, making option C the correct answer.

Question 5

How much money could Louie borrow if he can afford to make monthly payments of $350 for four years at an interest rate of 9% compounded monthly?
A) $14,065
B) $13,593
C) $10,752
D) $8,915
E) $3,827

Accepted Answer

The correct answer is A because $14,065 is the amount of money that Louie can borrow if he can afford to make monthly payments of $350 for four years at an interest rate of 9% compounded monthly.

Question 6

Calculate the present value of an ordinary annuity consisting of payments of $5,000 each, made at the end of every three months for six years. Assume that money is worth 7.2% compounded quarterly.
A) $46,070
B) $76,295
C) $96,748
D) $105,186
E) $122,517

Accepted Answer

The answer of Calculate the present value of an ordinary...

Question 7

Marvin has determined that he can save at least $6 per day by quitting smoking and cutting out one cup of coffee or one can of pop per day. Therefore, he has decided to make contributions of $175 to his Retirement Savings Plan (RSP) at the end of each month for 35 years. He anticipates that his RSP will earn 13.2% compounded monthly. He is 20 years old now and therefore he will be only 55 when this plan is completed. How much money will be in his RSP when he is 55 years of age?
A) Less than $500,000
B) Between $500,000 and $1,000,000
C) Between $1,000,000 and $1,500,000
D) Between $1,500,000 and $2,000,000
E) More than $2,000,000

Accepted Answer

The future value of Marvin's RSP can be calculated using the formula for the future value of a series: FV = P * [((1 + r)^n - 1) / r], where P is the payment amount ($175), r is the monthly interest rate (13.2% per year or 0.132 / 12 per month), and n is the total number of payments (35 years * 12 months/year = 420 payments). Plugging in the values: FV = 175 * [((1 + 0.011)^420 - 1) / 0.011], which results in a value between $1,500,000 and $2,000,000.

Question 8

What amount could you borrow at 6.6% compounded monthly if you can afford to make monthly payments of $775 for 25 years?
A) $40,688
B) $92,867
C) $101,106
D) $113,725
E) $217,155

Accepted Answer

The answer of What amount could you borrow at 6.6%...

Question 9

At the end of every six months for the last six years Vincent has borrowed $1,000 from Charley at an interest rate of 11% compounded semi-annually. He has not made any payments to reduce his debt. How much, including interest, does Vincent owe Charley now?
A) $19,920
B) $16,386
C) $22,714
D) $8,618
E) $15,536

Accepted Answer

The answer of At the end of every six months...

Question 10

Terri and Larry plan to invest $5,000 at the end of each year in an individual retirement account earning a rate of return of 11% compounded annually. What will be the value of the account after 15 years?
A) $119,864
B) $172,027
C) $198,215
D) $214,739
E) $359,543

Accepted Answer

The value of the account after 15 years can be calculated using the future value of an annuity formula: 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 periods. Plugging in the values: FV = $5,000 * [((1 + 0.11)^15 - 1) / 0.11] = $172,027.

Question 11

Roger spends $60 per month on beer and $60 per month on cigarettes. He is going to quit smoking and cut his beer expense in half by making his own beer at the local U-Brew. At the end of every month the money he saves is going to go into an investment plan earning 12% compounded monthly. How much money should he have after 40 years?
A) $250,560
B) $443,946
C) $892,605
D) $1,058,830
E) $1,411,772

Accepted Answer

Roger saves $60 from quitting smoking and $30 from cutting his beer expense, totaling $90 saved per month. Using the future value of an annuity formula for monthly compounding, FV = P * [(1 + r)^nt - 1] / r, where P = $90, r = 0.12/12, n = 12, and t = 40, the future value is approximately $1,058,830.

Question 12

Sparky will invest $7,500 into his RRSP at the end of each year for 30 years. How much more money will he have in 30 years if he is able to earn 13% compounded annually rather than 11% compounded annually?
A) $149,266
B) $219,899
C) $304,261
D) $589,114
E) $706,338

Accepted Answer

The future value of an annuity formula is used to calculate the total amount of money accumulated after making regular deposits. The formula is FV = P * [(1 + r)^n - 1] / r, where P is the annual deposit, r is the interest rate, and n is the number of years. Calculating for both 13% and 11% and finding the difference gives $706,338.

Question 13

What amount would you have to invest now at 10% compounded semi-annually in order to make withdrawals of $3,500 every half-year for eight years? The first withdrawal is to be made in six months.
A) $52,224
B) $28,000
C) $37,932
D) $36,126
E) $8,255

Accepted Answer

The correct answer is found by calculating the present value of an annuity due to the semi-annual withdrawals and the semi-annual compounding interest. Using the formula for the present value of an annuity due, where the interest rate per period is 5% (10% annual rate compounded semi-annually), the number of periods is 16 (8 years, with withdrawals every half-year), and the payment per period is $3,500, the calculation gives the present value as approximately $37,932. This accounts for the fact that each withdrawal is discounted back to the present value at the semi-annual rate, and the first withdrawal occurs in six months, aligning with the annuity due formula.

Question 14

Valerie has made investments of $10,000 at the end of every three months for the last 8 years. She has earned 11% compounded quarterly? What is the value of the investments today?
A) $97,427
B) $211,003
C) $320,000
D) $460.792
E) $502,699

Accepted Answer

The future value of an annuity formula is used here: FV = Pmt * [((1 + r)^nt - 1) / r], where Pmt = $10,000, r = 0.11/4, n = 4, and t = 8. Plugging in these values gives the future value of the investments as approximately $502,699.

Question 15

What amount would you have to invest now at 7% compounded annually in order to make withdrawals of $20,000 once per year for 25 years? The first withdrawal is to be made one year from now.
A) $233,072
B) $1,264,981
C) $544,343
D) $197,226
E) $427,561

Accepted Answer

The correct answer is A because the present value of an annuity is calculated using the formula PV = PMT * [1 - (1 + r)^-n] / r, where PV is the present value, PMT is the annual payment, r is the annual interest rate, and n is the number of years. In this case, PMT = $20,000, r = 7%, and n = 25. Plugging these values into the formula, we get PV = $20,000 * [1 - (1 + 0.07)^-25] / 0.07 = $233,072.

Question 16

What amount will an ordinary annuity be worth in 25 years if quarterly payments of $1,750 are made and the interest rate is 14% compounded quarterly for the first 15 years and 10% compounded quarterly for the final 10 years?
A) $384,999
B) $461,859
C) $1,509,570
D) $1,062,754
E) $1,041,360

Accepted Answer

To solve this, we break the problem into two parts because the interest rate changes after 15 years. First, calculate the future value of the annuity for the first 15 years with a 14% annual interest rate compounded quarterly. Then, take that amount and calculate what it will grow to in the next 10 years with a 10% annual interest rate compounded quarterly, while continuing the quarterly payments of $1,750.For the first 15 years:- Quarterly interest rate = 14% / 4 = 3.5%- Number of quarters = 15 * 4 = 60Using the future value of an annuity formula: $FV = P \times \frac{(1 + r)^n - 1}{r}$Where:- $FV$ is the future value of the annuity.- $P$ is the payment amount per period ($1,750).- $r$ is the interest rate per period (3.5% or 0.035 as a decimal).- $n$ is the total number of payments (60).$FV_{15years} = 1750 \times \frac{(1 + 0.035)^{60} - 1}{0.035}$For the next 10 years:- Quarterly interest rate = 10% / 4 = 2.5%- Number of quarters = 10 * 4 = 40We first calculate the future value of the amount accumulated in the first 15 years without additional payments, and then calculate the future value of the annuity for the next 10 years with the $1,750 quarterly payments.$FV_{total} = FV_{15years} \times (1 + 0.025)^{40} + 1750 \times \frac{(1 + 0.025)^{40} - 1}{0.025}$This calculation is complex and typically requires a financial calculator or spreadsheet software to compute accurately. The correct answer, after performing these calculations, is approximately $1,041,360, which corresponds to option E.

Question 17

Sara quit smoking and saves $80 per month previously spent on cigarettes. She invests the money at 5% compounded monthly. How much will she have in 10 years?
A) $7,542.51
B) $17,919.63
C) $12,422.58
D) $11,898.88
E) $12,474.34

Accepted Answer

The future value of a series of monthly investments can be calculated using the future value of an annuity formula: FV = P * [((1 + r)^nt - 1) / r], where P is the monthly investment ($80), r is the monthly interest rate (5% annual, so 0.05/12 per month), n is the number of times the interest is compounded per year (12), and t is the number of years (10). Plugging in these values gives approximately $12,422.58.

Question 18

At the end of every year for 45 years Sabrina invested $500 into her retirement plan. The plan has earned 13% compounded annually over the 45 years. She made the last deposit today. How much money has she accumulated?
A) $1,783,603
B) $937,082
C) $480,583
D) $318,675
E) $157,950

Accepted Answer

Sabrina's investment is a future value of an annuity problem. Using the formula for the future value of an annuity compounded annually: FV = P * [(1 + r)^n - 1] / r, where P = $500, r = 0.13, and n = 45, the accumulated amount is approximately $937,082.

Question 19

What is the future value of a series of 15 annual payments of $750 starting in one year and earning 7% compounded annually?
A) $6,831
B) $12,038
C) $17,673
D) $18,847
E) $32,848

Accepted Answer

The future value of an annuity is calculated using the formula:FV = PMT * [(1 + r)^n - 1] / rwhere:PMT is the annual paymentr is the annual interest raten is the number of yearsIn this case, PMT = $750, r = 7%, and n = 15. Plugging these values into the formula, we get:FV = $750 * [(1 + 0.07)^15 - 1] / 0.07= $750 * [2.853 - 1] / 0.07= $750 * 1.853 / 0.07= $18,847Therefore, the future value of the annuity is $18,847.

Question 20

If you want to purchase an annuity providing an income of $2,000 at the end of each month for five years, how much will it cost if the purchase funds earn 18% compounded monthly?
A) $192,429.30
B) $78,760.54
C) $80,681.00
D) $4,886.44
E) $818.60

Accepted Answer

The cost of purchasing an annuity can be calculated using the present value formula for annuities. Given an annuity that pays $2,000 at the end of each month for five years (60 months) with an interest rate of 18% compounded monthly, the monthly interest rate is 18%/12 = 1.5%. Using the present value of an annuity formula: $P = PMT \times \left(\frac{1 - (1 + r)^{-n}}{r}\right)$, where PMT = $2,000, r = 0.015 (1.5%), and n = 60, the calculation yields approximately $78,760.54.

Quiz 10: Annuities: Future Value and Present Value

Jennifer already has $15,500 saved for a down payment for a house and she plans to save another $400 at the end of each month for the next three years. If she earns 8.4% compounded monthly how large will her down payment be in three years?

How much money would you have at the end of 10 years if you made deposits of $4,000 at the end of every three months into an investment that accumulated at 9% compounded quarterly?

How much money would you have at the end of five years if you made deposits of $450 at the end of every month into an investment that accumulated at 18% compounded monthly?

How much money could Louie borrow if he can afford to make monthly payments of $350 for four years at an interest rate of 9% compounded monthly?

Calculate the present value of an ordinary annuity consisting of payments of $5,000 each, made at the end of every three months for six years. Assume that money is worth 7.2% compounded quarterly.

What amount could you borrow at 6.6% compounded monthly if you can afford to make monthly payments of $775 for 25 years?

At the end of every six months for the last six years Vincent has borrowed $1,000 from Charley at an interest rate of 11% compounded semi-annually. He has not made any payments to reduce his debt. How much, including interest, does Vincent owe Charley now?

Terri and Larry plan to invest $5,000 at the end of each year in an individual retirement account earning a rate of return of 11% compounded annually. What will be the value of the account after 15 years?

Sparky will invest $7,500 into his RRSP at the end of each year for 30 years. How much more money will he have in 30 years if he is able to earn 13% compounded annually rather than 11% compounded annually?

What amount would you have to invest now at 10% compounded semi-annually in order to make withdrawals of $3,500 every half-year for eight years? The first withdrawal is to be made in six months.

Valerie has made investments of $10,000 at the end of every three months for the last 8 years. She has earned 11% compounded quarterly? What is the value of the investments today?

What amount would you have to invest now at 7% compounded annually in order to make withdrawals of $20,000 once per year for 25 years? The first withdrawal is to be made one year from now.

What amount will an ordinary annuity be worth in 25 years if quarterly payments of $1,750 are made and the interest rate is 14% compounded quarterly for the first 15 years and 10% compounded quarterly for the final 10 years?

Sara quit smoking and saves $80 per month previously spent on cigarettes. She invests the money at 5% compounded monthly. How much will she have in 10 years?

At the end of every year for 45 years Sabrina invested $500 into her retirement plan. The plan has earned 13% compounded annually over the 45 years. She made the last deposit today. How much money has she accumulated?

What is the future value of a series of 15 annual payments of $750 starting in one year and earning 7% compounded annually?

If you want to purchase an annuity providing an income of $2,000 at the end of each month for five years, how much will it cost if the purchase funds earn 18% compounded monthly?