Question 1

Column 3 is an interest table for the:

Accepted Answer

The answer of Column 3 is an interest table for...

Question 2

Shelley wants to cash in her winning lottery ticket. She can either receive ten, $100,000 semiannual payments starting today, or she can receive a lump-sum payment now based on a 6% annual interest rate. What is the equivalent lump-sum payment?

Accepted Answer

The equivalent lump-sum payment is calculated using the present value of an annuity due formula, which considers the 6% annual interest rate compounded semiannually (3% per period) for 10 periods. The calculation provided uses the correct present value annuity due factor (8.78611) for these parameters.

Question 3

Ajax Company purchased a five-year certificate of deposit for their building fund in the amount of $220,000. How much should the certificate of deposit be worth at the end of five years if interest is compounded at an annual rate of 9%?

Accepted Answer

Using the formula for compound interest, we can calculate the final value (FV) of the certificate of deposit after five years:
FV = $220,000 x (1 + 0.09)^5
FV = $220,000 x 1.53862*
FV = $338,496
Therefore, the certificate of deposit should be worth $338,496 at the end of five years if interest is compounded at an annual rate of 9%. The correct answer is D.

Question 4

On January 1, 2009, you are considering making an investment that will pay three annual payments of $10,000. The first payment is not expected until December 31, 2012. You are eager to earn 3%. What is the present value of the investment on January 1, 2009?

Accepted Answer

Using the present value of an annuity formula, we can calculate the present value of the three payments: 
PVA = $10,000 x (1 - 1/(1+0.03)^3)/0.03 = $25,886

Therefore, the present value of the investment on January 1, 2009, is $25,886. The best choice is B.

Question 5

Debbie has $368,882 accumulated in a 401K plan. The fund is earning a low, but safe, 3% a year. The withdrawals will take place annually starting today. How soon will the fund be exhausted if Debbie withdraws $30,000 each year?

Accepted Answer

The present value of an annuity due formula is used to determine how long the funds will last. With a present value of $368,882, annual withdrawals of $30,000, and an interest rate of 3%, the fund will last approximately 15 years.

Question 6

Reba wishes to know how much would be in her savings account if she deposits a given sum in an account and leaves it there at 6% interest for five years. She should use a table for the:

Accepted Answer

Reba is only depositing a one-time amount and leaving it in the account for five years. Therefore, she is looking for the future value of that initial deposit, not an annuity. The future value of 1 table will allow her to calculate the value of her deposit after five years with 6% interest.

Question 7

Column 5 is an interest table for the:

Accepted Answer

The answer of Column 5 is an interest table for...

Question 8

Column 1 is an interest table for the:

Accepted Answer

The answer of Column 1 is an interest table for...

Question 9

On January 1, 2009, you are considering making an investment that will pay three annual payments of $10,000. The first payment is not expected until December 31, 2011. You are eager to earn 3%. What is the present value of the investment on January 1, 2009?

Accepted Answer

To calculate present value, we need to use the formula: PV = PMT x (1 - 1/(1+r)^n) / r
Plugging in the given values, we get: PV = $10,000 x (1 - 1/(1+0.03)^3) / 0.03
Solving this equation gives us a present value of $26,662, which is option A.

Question 10

At the end of each quarter, Patti deposits $500 into an account that pays 12% interest compounded quarterly. How much will Patti have in the account in three years?

Accepted Answer

The future value of an annuity formula is used here: FVA = Pmt * [(1 + r)^nt - 1] / r. Patti deposits $500 quarterly, the interest rate per quarter is 3% (12% annually), and there are 12 quarters in 3 years. Using the future value annuity factor (14.1920) for these parameters, the calculation is $500 * 14.1920 = $7,096.

Question 11

Column 4 is an interest table for the:

Accepted Answer

The answer of Column 4 is an interest table for...

Question 12

Sondra deposits $2,000 in an IRA account on April 15, 2009. Assume the account will earn 3% annually. If she repeats this for the next nine years, how much will she have on deposit on April 14, 2019?

Accepted Answer

Using the formula for future value of an annuity due, we get: FVAD = $2,000 x 11.8078* = $23,616. Therefore, Sondra will have $23,616 on deposit on April 14, 2019.

Question 13

Jose wants to cash in his winning lottery ticket. He can either receive five, $5,000 semiannual payments starting today, or he can receive a lump-sum payment now based on a 6% annual interest rate. What would be the lump-sum payment?

Accepted Answer

The lump-sum payment is calculated using the present value of an annuity due formula. The present value of the annuity due (PVAD) is $23,586, which matches choice A.

Question 14

Micro Brewery borrows $300,000 to be paid off in three years. The loan payments are semiannual with the first payment due in six months, and interest is at 6%. What is the amount of each payment?

Accepted Answer

The loan payments are semiannual, meaning there will be six payments in total (three years x 2 payments per year). Using the present value of an annuity formula, we can find that each payment will be $55,379.

Question 15

A firm leases equipment under a capital lease (analogous to an installment purchase) that calls for twelve semiannual payments of $39,014.40. The first payment is due at the inception of the lease. The annual rate on the lease is 6%. What is the value of the leased asset at inception of the lease?

Accepted Answer

Using the PVAD formula: PVAD = PMT x [1 - 1/(1 + r)^n]/r
where PMT = $39,014.40, r = 3% (semiannual rate), and n = 12 (number of semiannual periods)
PVAD = $39,014.40 x [1 - 1/(1 + 0.03)^12]/0.03
PVAD = $39,014.40 x 10.25262
PVAD = $400,000
Therefore, the value of the leased asset at inception of the lease is $400,000, which is option B.

Question 16

Jimmy has $255,906 accumulated in a 401K plan. The fund is earning a low, but safe, 3% a year. The withdrawals will take place at the end of each year starting a year from now. How soon will the fund be exhausted if Jimmy withdraws $30,000 each year?

Accepted Answer

The present value of an annuity factor for 10 years at 3% interest is approximately 8.5302, which matches the given scenario. Thus, the fund will be exhausted in 10 years with annual withdrawals of $30,000.

Question 17

Rosie's Florist borrows $300,000 to be paid off in six years. The loan payments are semiannual with the first payment due in six months, and interest is at 6%. What is the amount of each payment?

Accepted Answer

Using a financial calculator, we can find that the present value of the loan is $300,000. The loan term is 6 years or 12 semi-annual periods. The interest rate is 6% or 3% per semi-annual period. Using the formula for the present value of an annuity, we can calculate the amount of each payment to be $30,139. Therefore, the best choice is C.

Question 18

Column 2 is an interest table for the:

Accepted Answer

The answer of Column 2 is an interest table for...

Question 19

Column 6 is an interest table for the:

Accepted Answer

The answer of Column 6 is an interest table for...

Question 20

At the end of the next four years, a new machine is expected to generate net cash flows of $8,000, $12,000, $10,000, and $15,000, respectively. What are the cash flows worth today if a 3% interest rate properly reflects the time value of money in this situation?

Accepted Answer

The present value of the cash flows is calculated using the given discount factors for each year, resulting in a total of $41,556.

Quiz 6: Time Value of Money Concepts