Question 1

Your bank offers a 10-year certificate of deposit (CD) that pays 6.5% interest, compounded annually.If you invest $2,000 in the CD, how much will you have when it matures?

Accepted Answer

A

Question 2

A time line is meaningful even if all cash flows do not occur annually.

Accepted Answer

A time line allows for the visual representation of cash flows over time, even if they occur at different intervals. It is a useful tool for analyzing and comparing different investment options, regardless of their payment frequency.

Question 3

Time lines can be constructed in situations where some of the cash flows occur annually but others occur quarterly.

Accepted Answer

Time lines can easily depict cash flows that occur at different intervals such as annually or quarterly. The time line will simply have more tick marks and shorter periods for the quarterly cash flows.

Question 4

Time lines cannot be constructed for annuities unless all the payments occur at the end of the periods.

Accepted Answer

Time lines can be constructed for annuities with payments made at the beginning or end of the periods. However, there are different conventions for illustrating these types of annuities on time lines.

Question 5

JG Asset Services is recommending that you invest $1,500 in a 5-year certificate of deposit (CD) that pays 3.5% interest, compounded annually.How much will you have when the CD matures?

Accepted Answer

The amount at maturity can be calculated using the formula for compound interest: A = P(1 + r/n)^(nt), where A is the amount of money accumulated after n years, including interest, P is the principal amount ($1,500), r is the annual interest rate (3.5% or 0.035), n is the number of times that interest is compounded per year (1, since it's compounded annually), and t is the time the money is invested for (5 years). Plugging in the values: A = 1500(1 + 0.035/1)^(1*5) = 1500(1.035)^5 ≈ $1,781.53.

Question 6

Cyberhost Corporation's sales were $225 million last year.If sales grow at 6% per year, how large (in millions) will they be 5 years later?

Accepted Answer

Using the formula for compound annual growth rate (CAGR), we can calculate that the sales after 5 years will be:

Sales after 5 years = $225 million * (1 + 0.06)^5 = $301.10 million

Therefore, the best choice is C.

Question 7

Time lines cannot be constructed in situations where some of the cash flows occur annually but others occur quarterly.

Accepted Answer

Time lines can still be constructed in situations where cash flows occur at different intervals, such as annually and quarterly. The time line would simply need to use appropriate markings or tick marks to represent the different periods of time.

Question 8

How much would Roderick have after 6 years if he has $500 now and leaves it invested at 5.5% with annual compounding?

Accepted Answer

The answer of How much would Roderick have after 6...

Question 9

Some of the cash flows shown on a time line can be in the form of annuity payments while others can be uneven amounts.

Accepted Answer

It is possible for some cash flows to be in the form of annuity payments, which are equal periodic payments, while others can be uneven amounts.

Question 10

Time lines can be constructed for annuities where the payments occur at either the beginning or the end of the periods.

Accepted Answer

A time line can be constructed for annuities with payments at either the beginning (annuity due) or the end (ordinary annuity) of the periods.

Question 11

How much would $1, growing at 3.5% per year, be worth after 75 years?

Accepted Answer

The answer of How much would $1, growing at 3.5%...

Question 12

Ellen now has $125.How much would she have after 8 years if she leaves it invested at 8.5% with annual compounding?

Accepted Answer

We can use the formula for compound interest to find the final amount:

A = P(1 + r/n)^(nt)

Where:
A = final amount
P = initial amount
r = annual interest rate (as a decimal)
n = number of times interest is compounded per year
t = time in years

Plugging in the given values, we get:

A = 125(1 + 0.085/1)^(1*8)
A = 125(1.085)^8
A = $240.08

Therefore, Ellen would have $240.08 after 8 years if she leaves her money invested. The answer is D.

Question 13

Cochrane Associate's net sales last year were $525 million.If sales grow at 7.5% per year, how large (in millions) will they be 8 years later?

Accepted Answer

We can solve this using the formula for compound interest:

A = P(1 + r/n)^(nt)

where:
A = final amount
P = initial amount
r = annual interest rate as a decimal
n = number of times interest is compounded per year
t = number of years

In this case, the initial amount (P) is $525 million, the annual interest rate (r) is 7.5% or 0.075 as a decimal, the number of times interest is compounded per year (n) is 1, and the number of years (t) is 8.

Plugging in these values:

A = 525(1 + 0.075/1)^(1*8)
A = 525(1.075)^8
A = $936.33 million

Therefore, the answer is choice C ($936.33 million).

Question 14

Starting to invest early for retirement increases the benefits of compound interest.

Accepted Answer

Compound interest allows for earnings on both the initial investment and the accumulated interest. Starting to invest early allows for more time for the interest to compound, resulting in a larger retirement fund.

Question 15

A time line is not meaningful unless all cash flows occur annually.

Accepted Answer

A time line can still be meaningful if cash flows occur at different intervals, such as quarterly or monthly. However, it may require more complex calculations or adjustments to account for the timing of the cash flows.

Question 16

Some of the cash flows shown on a time line can be in the form of annuity payments but none can be uneven amounts.

Accepted Answer

Some of the cash flows on a time line can indeed be in the form of annuity payments (which are equal payments made at regular intervals), but cash flows can also be uneven amounts, representing irregular payments or receipts.

Question 17

The greater the number of compounding periods within a year, then (1) the greater the future value of a lump sum investment at Time 0 and (2) the smaller the present value of a given lump sum to be received at some future date.

Accepted Answer

This is due to the effect of compounding on interest earned. More compounding periods mean more frequent interest earned and added to the investment, resulting in a higher future value. On the other hand, the present value decreases because the interest earned from the investment is spread out over more compounding periods, resulting in a smaller lump sum received in the future being worth less in present dollars.

Question 18

Starting to invest early for retirement reduces the benefits of compound interest.

Accepted Answer

Starting to invest early for retirement actually maximizes the benefits of compound interest, as the longer the money is invested, the more time it has to grow through the power of compounding.

Question 19

How much would $100, growing at 5% per year, be worth after 75 years?

Accepted Answer

The answer of How much would $100, growing at 5%...

Question 20

The greater the number of compounding periods within a year, then (1) the greater the future value of a lump sum investment at Time 0 and (2) the greater the present value of a given lump sum to be received at some future date.

Accepted Answer

The greater number of compounding periods increases the future value of a lump sum investment due to more frequent application of interest, but it decreases the present value of a future lump sum because more compounding periods mean a higher effective discount rate is applied to the future sum, making its present value lower.

Quiz 4: Time Value of Money