Question 1

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

Accepted Answer

The future value of an ordinary annuity can be calculated using the formula: FV = P * [(1 + r)^n - 1] / r, where P is the payment amount, r is the interest rate, and n is the number of periods. Plugging in the values: FV = 500 * [(1 + 0.08)^8 - 1] / 0.08 = $5,318.31.

Question 2

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?

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 payment amount, r is the interest rate per period, and n is the total number of payments. Here, PMT = $600, r = 6%/4 = 1.5% = 0.015, and n = 4*4 = 16. Plugging these values into the formula gives the present value as approximately $8,478.76.

Question 3

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 in order to receive a series of equal payments in the future.

Question 4

Payments in annuities must be made:

Accepted Answer

The answer of Payments in annuities must be made:
...

Question 5

An annuity is:

Accepted Answer

An annuity is a stream of payments, typically made on a regular basis. It can be used for retirement income, insurance payments, or other purposes. Lotteries are not typically structured as annuities, as winners usually have the option to take a lump sum payment instead. An annuity can be made up of equal payments or varying amounts depending on the terms of the contract. Therefore, choice C is the best answer.

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

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?

Accepted Answer

The present value of an annuity formula is used to calculate how much Howard needs to invest today to withdraw $12,000 annually for 20 years at an 8% interest rate. The correct calculation gives approximately $117,817.77.

Question 8

A sinking fund:

Accepted Answer

A sinking fund is a fund set up to help meet a future obligation, such as the repayment of a loan. It involves regular contributions over time, rather than a lump sum payment. The money in the fund is typically invested and may or may not compound over time.

Question 9

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

Accepted Answer

The future value of the annuity is equal to the present value of the loan. The future value of the annuity can be calculated using the formula:FV = PMT * (((1 + r)^n - 1) / r)where:PMT is the annual paymentr is the annual interest raten is the number of yearsIn this case, the annual payment is $8,000, the annual interest rate is 5%, and the number of years is 12. Plugging these values into the formula, we get:FV = $8,000 * (((1 + 0.05)^12 - 1) / 0.05)FV = $8,000 * 15.9374246FV = $127,337.01Therefore, the amount of the original loan was $127,337.01.

Question 10

Ordinary annuity payments are made:

Accepted Answer

An ordinary annuity is a series of equal payments made at the end of each period, such as a mortgage payment at the end of each month or a quarterly dividend payment at the end of each quarter. Therefore, choice A is the correct answer as it describes when ordinary annuity payments are made. Choices B, C, and D are incorrect as they suggest specific payment frequencies, which may or may not be applicable to ordinary annuities. Choice E is also incorrect as it does not provide any useful information.

Question 11

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

Accepted Answer

An annuity due is essentially an ordinary annuity with payments made at the beginning of each period instead of the end. This means that with all other factors being equal, the present value of an annuity due will be higher than that of an ordinary annuity. Thus, the answer is A, Higher value.

Question 12

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

Accepted Answer

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

Question 13

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:

Accepted Answer

The answer of Ed Sloan invests $1,600 at the beginning...

Question 14

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

Accepted Answer

The future value of an ordinary annuity can be calculated using the formula: FV = Pmt * [((1 + r)^nt - 1) / r], where Pmt is the payment amount, r is the interest rate per period, n is the number of periods per year, and t is the number of years. Here, Pmt = $1,200, r = 0.04/4 = 0.01, n = 4, and t = 8. Plugging these values into the formula gives the future value as $44,992.88.

Question 15

Annuity due payments are made:

Accepted Answer

Annuity due payments are made at the beginning of the period. This means that the payment is made at the start of the period, such as the beginning of each month, instead of at the end of the period.

Question 16

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.

Accepted Answer

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

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

where PV is the present value (or the amount to be deposited today), PMT is the yearly payment ($18,000), r is the interest rate (9% or 0.09), and n is the number of payments (20).

Plugging in the values, we get:

PV = $18,000 * ((1 - (1 + 0.09)^(-20)) / 0.09)
PV = $164,313.82

Therefore, Abby Mia must deposit $164,313.82 today in order to receive yearly payments of $18,000 for 20 years at a rate of 9% compounded annually.

Question 17

Contingent annuities:

Accepted Answer

Contingent annuities do not have a fixed amount of payments and are dependent on certain conditions, such as the death of the annuitant.

Question 18

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):

Accepted Answer

First, we need to calculate the interest rate per period, which is 4% (8% divided by 2, since interest is compounded semiannually).

Next, we need to calculate the number of periods over 12 years, which is 24 (since there are two periods in a year - one every 6 months - for a total of 24 over 12 years).

Finally, we can use the formula for a sinking fund:

Payment per period = (Loan amount * i) / ((1 + i)^n - 1)

Where:
- Loan amount = $60,000
- i = 4%
- n = 24

Plugging these values into the formula, we get:

Payment per period = ($60,000 * 0.04) / ((1 + 0.04)^24 - 1) = $1,535.21

Therefore, the answer is B: $1,535.21.

Question 19

Joe Sullivan invests $9,000 at the end of each year for 20 years. The rate of interest Joe gets is 8% annually. The final value of Joe's investment at the end of the 20th year on this ordinary annuity is

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 * ((1 + r)^n - 1) / r
where PMT is the yearly payment, r is the annual interest rate, and n is the number of periods. In this case, we have PMT = $9,000, r = 8%, and n = 20. Plugging in the numbers, we get:
FV = $9,000 * ((1 + 0.08)^20 - 1) / 0.08
FV = $411,857.68
Therefore, the best choice is C, with the final value of Joe's investment being $411,857.68.

Question 20

An annuity due can use the ordinary annuity formula if the ordinary annuity formula is adjusted:

Accepted Answer

An annuity due requires payments at the beginning of each period. To adjust the ordinary annuity formula (which assumes end-of-period payments) for an annuity due, you multiply the result by (1+i), where i is the interest rate per period.

Quiz 20: Annuities and Sinking Funds