Question 1

Match the following terms with their definitions.
-Compound

Accepted Answer

Compounding refers to the process where interest is calculated on the initial principal, which also includes all of the accumulated interest from previous periods on a deposit or loan.

Question 2

Anne Katz, the owner of Katz Sport Shop, lends $8,000 to Shelley Slater to help her open an art shop. Shelley plans to repay Anne at the end of eight years with interest compounded semiannually at 8%. At the end of eight years, Anne will receive (use the tables in the handbook):

Accepted Answer

The future value of a loan of $8,000 at 8% compounded semiannually for eight years is $14,984.

Question 3

Trisha Long wants to buy a boat in five years. She estimates the boat will cost $15,000 at that time. What must Trisha deposit today in an account earning 5% annually to have enough to buy the boat in five years?

Accepted Answer

The answer of Trisha Long wants to buy a boat...

Question 4

Interest on $2,630 at 3% compounded semiannually for five years is:

Accepted Answer

We can use the formula A=P(1+r/n)^(nt) where:
A = the amount of money at the end of the investment period
P = the principal (starting amount)
r = the annual interest rate (as a decimal)
n = the number of times per year the interest is compounded
t = the number of years

Plugging in the given values, we get:

A = 2630(1+0.03/2)^(2*5)
A = 2630(1.015)^10
A = 2630(1.162752)
A = $3056.58

To find the interest earned, we subtract the principal from the final amount:

Interest = $3056.58 - $2630
Interest = $426.58

Since the interest is not compounded annually, we cannot simply use the simple interest formula. Therefore, the only answer choice that is close to our calculated interest is option D, $422.12.

Question 5

Jim Moore opens a new savings account. He deposits $12,000 at 12% compounded semiannually. At the start of the fourth year, Jim deposits an additional $50,000 that is also compounded semiannually at 12%. At the end of six years, the balance in Jim Moore's account is (use the tables in the handbook):

Accepted Answer

The answer of Jim Moore opens a new savings account....

Question 6

Merle Fonda opened a new savings account. She deposited $40,000 at 10% compounded semiannually. At the start of the fourth year, Merle deposits an additional $20,000 that is also compounded semiannually at 10%. At the end of six years, the balance in Merle's account is (use the tables in the handbook):

Accepted Answer

Using the compound interest formula, we can find the balance after 6 years:

For the first 3 years:
A = P(1 + r/n)^(nt)
A = 40000(1 + 0.10/2)^(2*3)
A = 40000(1.05)^6
A = 67100.81

After the 3rd year, Merle deposits an additional $20,000. So the new principal is $60,000.
For the remaining 3 years:
A = P(1 + r/n)^(nt)
A = 60000(1 + 0.10/2)^(2*3)
A = 60000(1.05)^6
A = 104536.925

Therefore, the balance in Merle's account at the end of 6 years is:
$67,100.81 + $104,536.925 = $171,637.735

However, we need to round this amount to the nearest cent based on the tables in the handbook. The closest amount to $171,637.735 is $171,637.72, which corresponds to an answer of D ($98,636.72).

Question 7

Al Miler, the owner of Al's Garage, estimates that he will need $29,000 for new equipment in 15 years. Al decides that he will put aside the money now so that in 15 years the $29,000 will be available. His bank offers him 10% interest compounded semiannually. (Use the tables in the handbook.)Al must invest today:

Accepted Answer

The correct answer is A.The formula for the future value of an investment is:FV = PV * (1 + r/n)^(nt)where:FV is the future valuePV is the present valuer is the annual interest raten is the number of times per year that the interest is compoundedt is the number of yearsIn this case, we have:FV = $29,000r = 10% = 0.10n = 2 (since the interest is compounded semiannually)t = 15Substituting these values into the formula, we get:$29,000 = PV * (1 + 0.10/2)^(2*15)$29,000 = PV * (1.05)^30$29,000 = PV * 14.0159Dividing both sides by 14.0159, we get:PV = $2,070.16Therefore, Al must invest $2,070.16 today in order to have $29,000 in 15 years.

Question 8

Gracie Shay wants to buy a new Hummer in six years. Gracie estimates the cost of the Hummer will be $35,000. If she invests $22,000 now at a rate of 6% compounded quarterly, she:

Accepted Answer

The answer of Gracie Shay wants to buy a new...

Question 9

Ellen deposits $6,773 into an account earning 1% annually. After seven years what will Ellen's balance have grown to, including interest?

Accepted Answer

The answer of Ellen deposits $6,773 into an account earning...

Question 10

Match the following terms with their definitions.
-Rate

Accepted Answer

The answer of Match the following terms with their definitions.
-Rate
...

Question 11

Earl Miller deposited $25,000 at Y Bank at an interest rate of 12% compounded quarterly. (Use the tables in the handbook.)The effective rate (APY)is: (round to the nearest hundredth percent, if applicable)

Accepted Answer

The effective annual rate (APY) for an interest rate compounded quarterly can be calculated using the formula $APY = (1 + \frac{r}{n})^n - 1$, where $r$ is the annual nominal interest rate (expressed as a decimal), and $n$ is the number of compounding periods per year. For a 12% annual interest rate compounded quarterly, $r = 0.12$ and $n = 4$, so $APY = (1 + \frac{0.12}{4})^4 - 1 = (1 + 0.03)^4 - 1 ≈ 0.1255$ or 12.55%.

Question 12

Lisa Richter deposited $5,000 at 4% compounded semiannually for three years. At the beginning of the fourth year, Lisa deposited $2,500. What would her balance be at the end of five years assuming she is still earning 4% compounded semiannually?

Accepted Answer

Lisa's initial deposit grows for five years, and the additional deposit grows for two years. Calculating both and summing gives the final balance.

Question 13

Katie Hector wants to purchase a condo in Oxford, MS, in 20 years. The cost of the condo is expected to be $180,000. Assuming she can earn 6% annually, what should Katie deposit today?

Accepted Answer

To find out how much Katie needs to deposit today to have $180,000 in 20 years at an annual interest rate of 6%, we use the formula for the present value of a single sum: PV = FV / (1 + r)^n, where PV is the present value (what Katie needs to deposit today), FV is the future value ($180,000), r is the annual interest rate (6% or 0.06), and n is the number of years (20). Plugging in the numbers: PV = $180,000 / (1 + 0.06)^20 = $180,000 / (3.207) ≈ $56,124.

Question 14

Match the following terms with their definitions.
-Nominal rate

Accepted Answer

The nominal rate is the interest rate stated on a loan or investment agreement before any adjustments for compounding or fees.

Question 15

Match the following terms with their definitions.
-Quarterly

Accepted Answer

Quarterly means something that occurs four times per year.

Question 16

Mia Kaminsky wants to attend Riverside Community College. She will need to have $25,000 six years from today. Mia is wondering what she will have to put in the bank today so that she will have $25,000 six years from now. Her bank pays 6% compounded semiannually. Using the tables in the handbook, the amount Mia will have to deposit is:

Accepted Answer

Using the formula for compound interest, we have:

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

where A is the amount after t years, P is the principal (amount deposited), r is the annual interest rate (6%), n is the number of times the interest is compounded per year (2, since it is compounded semiannually), and t is the number of years (6).

We want to solve for P, so we rearrange the formula:

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

Substituting the given values, we have:

P = $25,000/(1 + 0.06/2)^(2*6) = $17,535.10

Therefore, Mia will have to deposit $17,535.10 today to have $25,000 six years from now. The answer is C.

Question 17

Jane is having difficulty deciding whether to put her savings in the Mystic Bank or in the Four Rivers Bank. Mystic offers a 12% rate compounded quarterly, and Four Rivers offers 14% compounded semiannually. Jane has $40,000 to invest and expects to withdraw the money at the end of five years. (Use the tables in the handbook.)The best deal is:

Accepted Answer

To determine the best deal, we calculate the future value of Jane's investment in both banks using the formula for compound interest: $A = P(1 + \frac{r}{n})^{nt}$, where $A$ is the amount of money accumulated after n years, including interest, $P$ is the principal amount (the initial amount of money), $r$ is the annual interest rate (decimal), $n$ is the number of times that interest is compounded per year, and $t$ is the time the money is invested for in years.For Mystic Bank: $P = \$40,000$, $r = 12\% = 0.12$, $n = 4$ (since interest is compounded quarterly), and $t = 5$ years.$$A_{Mystic} = 40000(1 + \frac{0.12}{4})^{4*5}$$For Four Rivers Bank: $P = \$40,000$, $r = 14\% = 0.14$, $n = 2$ (since interest is compounded semiannually), and $t = 5$ years.$$A_{FourRivers} = 40000(1 + \frac{0.14}{2})^{2*5}$$Without calculating the exact amounts, the general principle is that a higher interest rate compounded less frequently can still yield a higher return than a lower interest rate compounded more frequently over the same period. Given the higher interest rate at Four Rivers (14% compounded semiannually) compared to Mystic (12% compounded quarterly), Four Rivers offers a better deal over the five-year period, assuming the difference in compounding frequency does not offset the higher rate advantage.

Question 18

Sam Monte deposits $21,500 into Legal Bank, which pays 6% interest that is compounded semiannually. Using the table in the handbook, what will Sam have in his account at the end of six years?

Accepted Answer

To calculate the future value of Sam's deposit, we use 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 ($21,500), r is the annual interest rate (6% or 0.06), n is the number of times that interest is compounded per year (semiannually, so n=2), and t is the time the money is invested for in years (6 years). Plugging in the values: A = $21,500(1 + 0.06/2)^(2*6) = $30,654.70.

Question 19

Match the following terms with their definitions.
-Semiannually

Accepted Answer

Semiannually means occurring twice a year, which matches definition B.

Question 20

Burton Bush wants to retire in Arizona when he is 80 years of age. Burton, who is now 55, believes he will need $500,000 to retire comfortably. To date, he has set aside no retirement money. If he gets an interest rate of 6% compounded annually, he will have to invest today (use the tables in the handbook):

Accepted Answer

Using the present value formula:
PV = FV / (1 + r)^n
PV = 500,000 / (1 + 0.06)^25
PV = 116,496.83
Therefore, Burton will have to invest $116,500 today to have $500,000 when he is 80. The closest answer choice is D.

Quiz 12: Compound Interest and Present Value

Match the following terms with their definitions. -Compound

Anne Katz, the owner of Katz Sport Shop, lends $8,000 to Shelley Slater to help her open an art shop. Shelley plans to repay Anne at the end of eight years with interest compounded semiannually at 8%. At the end of eight years, Anne will receive (use the tables in the handbook) :

Trisha Long wants to buy a boat in five years. She estimates the boat will cost $15,000 at that time. What must Trisha deposit today in an account earning 5% annually to have enough to buy the boat in five years?

Interest on $2,630 at 3% compounded semiannually for five years is:

Gracie Shay wants to buy a new Hummer in six years. Gracie estimates the cost of the Hummer will be $35,000. If she invests $22,000 now at a rate of 6% compounded quarterly, she:

Ellen deposits $6,773 into an account earning 1% annually. After seven years what will Ellen's balance have grown to, including interest?

Match the following terms with their definitions. -Rate

Earl Miller deposited $25,000 at Y Bank at an interest rate of 12% compounded quarterly. (Use the tables in the handbook.) The effective rate (APY) is: (round to the nearest hundredth percent, if applicable)

Lisa Richter deposited $5,000 at 4% compounded semiannually for three years. At the beginning of the fourth year, Lisa deposited $2,500. What would her balance be at the end of five years assuming she is still earning 4% compounded semiannually?

Katie Hector wants to purchase a condo in Oxford, MS, in 20 years. The cost of the condo is expected to be $180,000. Assuming she can earn 6% annually, what should Katie deposit today?

Match the following terms with their definitions. -Nominal rate

Match the following terms with their definitions. -Quarterly

Sam Monte deposits $21,500 into Legal Bank, which pays 6% interest that is compounded semiannually. Using the table in the handbook, what will Sam have in his account at the end of six years?

Match the following terms with their definitions. -Semiannually