Chapter 5 adaptive

If Rose wants to have $570,000 from a $226,000 investment after 12 years, the interest rate (to the nearest percent) she needs

8% $570,000 / $226.000 = 2.52 = Future value of 1 for 12 years at 8%

Why is the future value always more than the present value?

due to earned and accumulated interest

Kelly is trying to save $5,000. She currently has $3,960. Kelly wants to put the money in a CD at a bank that offers 3% interest on long-term CDs. What else does Kelly need to know to determine which CD she should choose?

how many time periods are needed to grow her money from $3,960 to $5,000

Given the following two examples: the present value of $1 for 10 periods at 8% per period, and the future value of $1 for 10 periods at 8% per period, which of the following statements would be true?

The future value of $1 for 10 periods at 8% per period would result in the greater value. The future value is always larger than the present value, because it moves forward and accounts for earned and accumulated interest. This is known as the process of accumulation. Whereas the present value moves backwards in time using the process of discounting.

Casey knows that the present value of the expected cash flows at her store is $67,800. She wants to determine the expected cash flow. What other information does she need?

the present value factor Casey will need to divide the known present value of expected cash flow of $67,800 by a present value factor to determine the expected cash flow.

In order to determine the market value of a long-term bond, the

present values of the interest annuity and the principal amount are combined.

Kara won $3,000,000, which will be paid after twenty years. If the interest rate is 5% compounded annually, the present value of the amount is

$1,130,667 $3,000,000 ÷ (FV of 1 for 20 periods at 5%) = $3,000,000 ÷ 2.6533 = $1,130,667.

Ron secured a loan for $9,800. The bank offered him a simple interest rate of 6% over a three-year period. If Ron pays the loan back in three years, what will be the total amount paid to the bank?

$11.564 In order to calculate interest, the principal should be multiplied by the interest rate, which should then all be multiplied by the number of periods. In this case, that would be: $9,800 X.06 X3 = $1,764. then to find the total amount paid back to the bank, you must add the loan amount and the interest amount: $9,800 + $1,764 = $11.564.

The interest rate on an investment is 10%. The investment itself pays $30,000 at the beginning of each year for the next 10 years. The amount paid for this investment would be

$202,771 In order to determine this answer, you must multiply the present value of the annuity due. In this case, that is: 6.759027 X $30,000 = $202,770.81, which rounds up to $202,771.

A new company is expected to have annual earnings received at year end of $39,000 for 15 years, with a resale value of $75,000 at the end of that time. The present value of an ordinary annuity at 10% for 15 periods is 7.60608. The present value of 1 at 10% for 15 periods is 0.23939. The future value of 1 at 10% for 15 periods is 4.17725. The present value for the company using a 10% discount rate is

$314,591 The present value of the annual earnings is $39,000x 7.60608 = $296,637.12. The present value of the resale value is $75.000 x 0.23939 = $17,954.25. Therefore, the total present value for the company is $296,637 + $17,954 = $314,591.

Caitlyn's company made an investment on January 1, 2020. The company will then receive $9,000 on the last day of each year for the Nex six years. In order to earn 12% on this investment, the most Caitlyn's company should invest on January 1, 2020 is

$37.003 Present value of an annuity due at 12% for 7 periods = 5.11141 - 1.000 = 4.11141 x9,000 = $37.003.

Carolyn is helping to save for her granddaughter's college fund. It will probably take 18 years before she is in college, and Carolyn estimates she will need to save $150,000. If she earns 6% per annum, the amount that should be deposited every year for the next 18 years beginning today is

$4,579 $150,000 ÷ Future value of an annuity due (6%, 18 periods) = $150,000 ÷ 32.75999 = $4,579.

For the next six years, Tina's company will invest $70,000 on the last day of every year (2020-2025). If the company is able to earn 12% on their investment, then the amount in the account on December 31, 2025 will be

$568,063 $70,000x (Future value of ordinary annuity for 6 periods at 12%) = $70,000 x8.11519 = $568,063.

Daniel runs a bakery. The cash flow estimate for the bakery is $95,600, with a 35% probability, and $60,500, with a 65% probability. The present value factor is 0.95238. Given this information, what is the expected cash flow?

$72,785 In order to determine the expected cash flow in this case, you need to multiply the cash flow estimate by the probability assessments, and then sum the results. In this case that would be: ($95,600x .35) + ($60,500x .65) = $72,785.

On July 1, 2020, the Rotund Corporation will issue $7.5 million 12% bonds. The bonds will pay interest semi-annually on June 30 and December 31 of each year. It takes the bonds ten years to mature, and at the time of issuance, the market interest rate for similar types of bonds was 8%. The expected selling price for the bonds will be

$9.538.574 ($7,500,000 x0.45639) + ($450,000x 13.59033) = 3,422,925 + 6,115,649 = $9.538.574

Marco has purchased a boat for $800,000, and is planning to lease it for 20 years. Annual lease payments will be required at the end of each year. If Marco needs to earn a return of 10%, then the annual rent will be

$93,968 In order to determine the annual rental, you must divide the cost by the present value for an ordinary annuity at 10% for 20 years (8.51356). In this case, that would be $800,000 / 8.51356 = $93,968 (rounded).

Carrie took out a $15,800 small business loan. By the end of the year, she had paid off the loan and paid a total of $17,696. Based on this information, what was the interest rate on Carrie's loan for the year?

12% To find the interest rate, you have to first determine how much the company paid in interest on the loan. In this case, that can be determined by subtracting the original loan amount from the total amount that was paid: $17,696 - $15,800 = $1,896. Then to find the interest rate, divide the amount of interest paid by the original loan amount: $1,896 / $15,800 = 12%.

If Sandy invests $160,000 at an annual interest rate of 4%, it will take blank years for the investment to grow to $324,000.

18 $324,000 ÷ $160,000 = 2.025 = FV of 1 at 4% for 18 periods

At the end of each year, Sally pays $9,800 for a machine she rents. The present value of an ordinary annuity factor for this agreement is 3.60478. The present value of the ordinary annuity in this case is

35.326.84 To find the present value of the ordinary annuity, you must multiply the rent payment by the present value of the ordinary annuity factor. In this case that is: $9,800 X3.60478 = $35.326.84

Which of the following is true of the future value of an ordinary annuity?

It will always be less than the future value of an annuity due.

Which of the following investments will result in the smallest future amount?

One that offers annual compounding.