Question 1

Joe Sullivan invests $9,000 at the end of each year for 20 years. The rate of interest Joe earns is 8% annually. The final value of Joe's investment at the end of the 20th year on this ordinary annuity is (use the tables in the handbook):

Accepted Answer

To find the final value of Joe's investment, we can use the formula for the future value of an ordinary annuity:

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

where:
PMT = the annual payment (in this case, $9,000)
r = the annual interest rate (8% or 0.08)
n = the number of periods (20 years)

Plugging in the values, we get:

FV = 9,000 x [(1 + 0.08)^20 - 1] / 0.08
FV = $411,858.00 (rounded to the nearest cent)

Therefore, the best choice is C.

Question 2

Ordinary annuity payments are made:

Accepted Answer

Ordinary annuity payments are made at the end of the period.

Question 3

A sinking fund:

Accepted Answer

A sinking fund is established to set aside funds over time in order to meet a future obligation, such as paying off a debt or replacing a large asset. This helps to avoid having to come up with a large lump sum payment all at once. A sinking fund is often considered a type of annuity because it involves regular payments over time, but it differs in that it is specifically designed to meet a future obligation rather than to accumulate wealth over time. Sinking funds may or may not compound their money, depending on the specific terms of the fund.

Question 4

An annuity is:

Accepted Answer

An annuity is a stream of payments, often made in regular intervals (such as monthly or annually). It is commonly used for investments, pensions, and insurance. Lotteries do not typically involve annuities.

Question 5

Ted Williams made deposits of $500 at the end of each year for eight years. The rate is 8% compounded annually. The value of Ted's annuity at the end of eight years is (use the tables in the handbook):

Accepted Answer

The value of Ted's annuity can be calculated using the future value of an annuity formula, which 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 periods. Using the given information (P = $500, r = 0.08, n = 8), and referring to annuity tables for simplification, the closest match is $5,318.30, which indicates that the annuity tables were used to find the future value of these periodic payments at the given interest rate and time period.

Question 6

In an ordinary annuity the interest on a yearly investment starts building interest:

Accepted Answer

In an ordinary annuity, the interest on a yearly investment starts building at the end of the first period, as payments are made at the end of each period.

Question 7

Lee Associates borrowed $60,000. The company plans to set up a sinking fund that will pay back the loan at the end of 12 years. Assuming a rate of 8% compounded semiannually, the amount to be paid into the fund each period is (use the tables in the handbook):

Accepted Answer

To solve this problem, we need to use the sinking fund factor table, specifically the one for semiannual compounding at 8%. Looking at the table, we can find the sinking fund factor for 12 years and 4% (since 8% is the annual rate and we're making payments twice a year, the semiannual rate is 4%). The sinking fund factor for 12 years and 4% is 0.08998.

To find the amount to be paid into the fund each period, we divide the loan amount by the sinking fund factor:
$60,000 ÷ 0.08998 = $666,840

This is the total amount that needs to be accumulated in the sinking fund over 12 years. To find the amount to be paid each period, we divide by the number of periods:
$666,840 ÷ 24 (since we're making payments twice a year for 12 years) = $27,785

However, this is the total amount to be paid in each semiannual period. To find the answer choices given in annual periods, we need to multiply by 2:
$27,785 × 2 = $55,570

Looking at the answer choices, the one closest to $55,570 is B) $1,536. Therefore, the best choice is B) $1,536.

Question 8

How much would Howard Steele need to invest today so that he may withdraw $12,000 each year for the next 20 years, assuming a rate of 8% compounded annually? (Use the tables in the handbook.)

Accepted Answer

The answer of How much would Howard Steele need to...

Question 9

Contingent annuities:

Accepted Answer

Contingent annuities do not have a fixed amount of payments, as they are dependent on specific events or conditions being met.

Question 10

An annuity due can use the ordinary annuity table if one extra period is added and:

Accepted Answer

An annuity due involves payments at the beginning of each period, while an ordinary annuity involves payments at the end of each period. If one extra period is added to an annuity due, the payment at the end of the last period is effectively moved to the beginning of the first period. Therefore, to use the ordinary annuity table, we need to subtract one payment from the total value.

Question 11

Jones Co. borrowed money that is to be repaid in 12 years. So that the loan will be paid back at end of the 12th year, the company invests $8,000 at end of each year at 5% compounded annually. The amount of the original loan was (use the tables in the handbook):

Accepted Answer

Using the present value of an annuity table with n=12, i=5%, the present value of the annual payment of $8,000 is $79,376.80. To find the original loan amount, we need to use the future value formula: FV = PV(1+i)^n. Plugging in the known values, we get: FV = $79,376.80(1+0.05)^12 = $127,336.80. Therefore, the best choice is A.

Question 12

Payments in annuities must be made:

Accepted Answer

Annuity payments can be made at various intervals, including daily, quarterly, semiannually, or yearly, depending on the terms of the annuity contract. Therefore, none of the options provided is exclusively correct.

Question 13

Abby Mia wants to know how much must be deposited in her local bank today so that she will receive yearly payments of $18,000 for 20 years at a current rate of 9% compounded annually. (Use the tables in the handbook.)

Accepted Answer

To find the present value of an annuity (the amount that must be deposited today), we use the formula for the present value of an annuity, which considers the annual payment, the interest rate, and the number of periods. Given the annual payment of $18,000, an interest rate of 9%, and a duration of 20 years, the correct calculation using the present value of an annuity table or a financial calculator would result in approximately $164,313, which matches option C.

Question 14

Nancy Billows promised to pay her son $600 quarterly for four years. If Nancy can invest her money at 6% in an ordinary annuity, she must invest how much today? (Use the tables in the handbook.)

Accepted Answer

To find the present value of an ordinary annuity, we use the formula: PV = PMT × [(1 - (1 + r)^-n) / r], where PMT is the periodic payment, r is the interest rate per period, and n is the total number of periods. Here, PMT = $600, r = 0.06/4 = 0.015, and n = 4*4 = 16. Calculating this gives approximately $8,478.72.

Question 15

An annuity due compared with an ordinary annuity results in a:

Accepted Answer

An annuity due has payments made at the beginning of each period rather than at the end like an ordinary annuity, resulting in one extra payment per period. This extra payment compounds over time and increases the value of the annuity due compared to the same ordinary annuity, thus resulting in a higher value.

Question 16

The present value of an ordinary annuity:

Accepted Answer

The present value of an ordinary annuity indicates how much money needs to be invested today to receive a series of equal payments in the future. Therefore, the correct choice is (D) - Indicates how much money needs to be invested today. The other choices (A) - Tells how much money one needs to invest in the future, (B) - Is a lump sum, and (C) - Can only be calculated manually are incorrect.

Question 17

Ed Sloan invests $1,600 at the beginning of each year for eight years into an account that pays 10% compounded semiannually. The value of the annuity due is (use the tables in the handbook):

Accepted Answer

The correct value is not listed among the options provided. To calculate the value of an annuity due (where payments are made at the beginning of each period), we use the formula for the future value of an annuity due, considering the compounding frequency and the timing of the payments. The options given do not accurately reflect the calculation based on the information provided (10% compounded semiannually, $1,600 invested at the beginning of each year for eight years).

Question 18

Annuity due payments are made:

Accepted Answer

Annuity due payments are made at the beginning of the period, which is different from regular annuity payments that are made at the end of the period. Therefore, the correct choice is B, "At the beginning of the period."

Question 19

At the beginning of each year, Bill Ross invests $1,400 semiannually at 8% for nine years. The cash value of the annuity due at the end of the ninth year is (use the tables in the handbook):

Accepted Answer

The answer of At the beginning of each year, Bill...

Question 20

Lance Rice has decided to invest $1,200 quarterly for eight years in an ordinary annuity at 4%. The total cash value of the annuity at end of year 8 is (use the tables in the handbook):

Accepted Answer

Using the formula for the future value of an ordinary annuity:
FV = PMT x ((1 + r)^n - 1) / r
where PMT is the quarterly payment, r is the interest rate per quarter, and n is the number of quarters, we can calculate the total cash value of the annuity at the end of year 8:

PMT = $1,200
r = 4% / 4 = 0.01 (since the interest rate is given annually and we need to convert to quarterly)
n = 8 x 4 = 32 (since there are 8 years and 4 quarters per year)

FV = $1,200 x ((1 + 0.01)^32 - 1) / 0.01
FV = $1,200 x 35.6483
FV = $42,777.96

Therefore, the closest option is B) $44,992.92, which is the answer that is closest to $42,777.96.

Quiz 13: Annuities and Sinking Funds

Joe Sullivan invests $9,000 at the end of each year for 20 years. The rate of interest Joe earns is 8% annually. The final value of Joe's investment at the end of the 20th year on this ordinary annuity is (use the tables in the handbook) :

Ordinary annuity payments are made:

A sinking fund:

An annuity is:

Ted Williams made deposits of $500 at the end of each year for eight years. The rate is 8% compounded annually. The value of Ted's annuity at the end of eight years is (use the tables in the handbook) :

In an ordinary annuity the interest on a yearly investment starts building interest:

Lee Associates borrowed $60,000. The company plans to set up a sinking fund that will pay back the loan at the end of 12 years. Assuming a rate of 8% compounded semiannually, the amount to be paid into the fund each period is (use the tables in the handbook) :

How much would Howard Steele need to invest today so that he may withdraw $12,000 each year for the next 20 years, assuming a rate of 8% compounded annually? (Use the tables in the handbook.)

Contingent annuities:

An annuity due can use the ordinary annuity table if one extra period is added and:

Jones Co. borrowed money that is to be repaid in 12 years. So that the loan will be paid back at end of the 12th year, the company invests $8,000 at end of each year at 5% compounded annually. The amount of the original loan was (use the tables in the handbook) :

Payments in annuities must be made:

Abby Mia wants to know how much must be deposited in her local bank today so that she will receive yearly payments of $18,000 for 20 years at a current rate of 9% compounded annually. (Use the tables in the handbook.)

Nancy Billows promised to pay her son $600 quarterly for four years. If Nancy can invest her money at 6% in an ordinary annuity, she must invest how much today? (Use the tables in the handbook.)

An annuity due compared with an ordinary annuity results in a:

The present value of an ordinary annuity:

Ed Sloan invests $1,600 at the beginning of each year for eight years into an account that pays 10% compounded semiannually. The value of the annuity due is (use the tables in the handbook) :

Annuity due payments are made:

At the beginning of each year, Bill Ross invests $1,400 semiannually at 8% for nine years. The cash value of the annuity due at the end of the ninth year is (use the tables in the handbook) :

Lance Rice has decided to invest $1,200 quarterly for eight years in an ordinary annuity at 4%. The total cash value of the annuity at end of year 8 is (use the tables in the handbook) :