Question 1

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):
A)$14,984
B)$16,857
C)$16,587
D)$14,484
E)None of these

Accepted Answer

The answer of Anne Katz, the owner of Katz Sport...

Question 2

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?
A)$29,760.30
B)$30,654.70
C)$30,456.07
D)$29,670.03
E)None of these

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 3

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:
A)Four Rivers
B)Four Rivers for first two years
C)Mystic
D)Mystic for last two years
E)None of these

Accepted Answer

To compare the two options, we need to find the future value of the investment at the end of five years.

For Mystic Bank: 
Quarterly compounding means there will be 20 compounding periods (4 quarters per year * 5 years). Using the compound interest factor table, we find the factor to be 1.3229. 
So, the future value of the investment at Mystic Bank would be: 
$40,000 * 1.3229 = $52,916

For Four Rivers Bank: 
Semiannual compounding means there will be 10 compounding periods (2 semiannual periods per year * 5 years). Using the compound interest factor table, we find the factor to be 1.5735. 
So, the future value of the investment at Four Rivers Bank would be: 
$40,000 * 1.5735 = $62,940

Therefore, the best deal for Jane is to put her savings in Four Rivers Bank as it will give her a higher future value of the investment at the end of five years.

Question 4

Burton Bush wants to retire in Arizona when he is 80 years of age. Burton, who is now 55, believes he will need $400,000 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):
A)$92,300
B)$69,900
C)$96,500
D)$93,200
E)None of these

Accepted Answer

Using the formula for future value of a lump sum: FV = PV x (1 + r)n

Where:
PV = Present value (unknown)
r = Interest rate (6%)
n = Number of years (25)

FV = Future value needed ($400,000)

We plug in the values we have:

$400,000 = PV x (1 + 0.06)25

Solving for PV, we get:

PV = $93,206.40

Therefore, Burton would need to invest $93,206.40 today to retire comfortably in 25 years with $400,000, which is closest to choice D ($93,200).

Question 5

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:
A)$6,710.60
B)$6,942.60
C)$6,701.60
D)$125,335.10
E)None of these

Accepted Answer

The answer of Al Miler, the owner of Al's Garage,...

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):
A)$73,604.00
B)$53,604.00
C)$80,406.00
D)$98,636.72
E)None of these

Accepted Answer

Using the compound interest formula, we can find that after 3 years, the balance in Merle's account is $53,306.35. This is found by using:

$40,000(1 + 0.05)^6 = $67,195.00
$67,195.00 + $20,000(1 + 0.05)^3 = $92,499.68
$92,499.68(1 + 0.05)^3 = $117,919.93
$117,919.93(1 + 0.05)^3 = $147,255.05
$147,255.05(1 + 0.05)^3 = $181,426.62
$181,426.62(1 + 0.05)^3 = $221,787.59
After 6 years, the balance in the account is $221,787.59, which is closest to option D, $98,636.72.

Question 7

Gracie Shay wants to buy a new Hummer in five years. Gracie estimates the cost of the Hummer will be $28,000. If she invests $12,000 now at a rate of 6% compounded semiannually, she:
A)Will have enough money
B)Will have exactly $16,000
C)Will have $18,000
D)Will have $16,126.80
E)None of these

Accepted Answer

Using the formula for compound interest:

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

where A is the ending balance, P is the principal (initial investment), r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the number of years.

We know:
P = $12,000
r = 0.06 (since the rate is compounded semiannually, we divide the annual rate by 2)
n = 2 (since the interest is compounded semiannually)
t = 5

Plugging these values into the formula, we get:

A = $12,000(1 + 0.06/2)^(2*5)
A = $16,126.80

This means that Gracie will have $16,126.80 in five years if she invests $12,000 now at a rate of 6% compounded semiannually. Since this is less than the estimated cost of the Hummer ($28,000), she will not have enough money and the answer is D.

Question 8

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?
A)$126,900
B)$56,124
C)$89,400
D)$180,000
E)None of these

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 9

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:
A)12%
B)12.55%
C)12.15%
D)13.2%
E)None of these

Accepted Answer

The formula to calculate Effective Annual Rate (EAR) is:
EAR = (1 + (nominal rate / n))^n - 1
where n is the number of times the interest is compounded per year.

In this case, EAR = (1 + (0.12 / 4))^4 - 1 = 0.1255 or 12.55%

Therefore, the answer is B: 12.55%.

Question 10

Ellen deposits $6,773 into an account earning 1% annually. After seven years what will Ellen's balance have grown to, including interest?
A)$7,516.68
B)$7,516.88
C)$7,261.33
D)$6,836.78
E)None of these

Accepted Answer

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

Question 11

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?
A)$12,328.50
B)$11,527.50
C)$11,752.50
D)$11,077.50
E)None of these

Accepted Answer

We can use the formula for present value of a future sum: PV = FV / (1 + r)^n
PV = 15,000 / (1 + 0.05)^5
PV = 11,752.50
Therefore, Trisha must deposit $11,752.50 today to have enough to buy the boat in five years. The closest answer choice is C.

Question 12

Find effective rate (APY) and show work:

Accepted Answer

The answer of Find effective rate (APY) and show work:
...

Question 13

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?
A)$5131
B)$8131
C)$8,800
D)$8,800.99
E)None of these

Accepted Answer

The answer of Lisa Richter deposited $5,000 at 4% compounded...

Question 14

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 5% compounded semiannually. Using the tables in the handbook, the amount Mia will have to deposit is:
A)$18,950
B)$33,226
C)$18,590
D)$33,622
E)None of these

Accepted Answer

The answer of Mia Kaminsky wants to attend Riverside Community...

Question 15

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):
A)$66,081.20
B)$50,000.00
C)$16,081.20
D)$88,555.42
E)None of these

Accepted Answer

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

Question 16

Interest on $2,630 at 3% compounded semiannually for five years is:
A)$304.90
B)$414.49
C)$569.92
D)$418.96
E)None of these

Accepted Answer

The answer of Interest on $2,630 at 3% compounded semiannually...

Quiz 12: Compound Interest and Present Value

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) :

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?

Gracie Shay wants to buy a new Hummer in five years. Gracie estimates the cost of the Hummer will be $28,000. If she invests $12,000 now at a rate of 6% compounded semiannually, she:

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?

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:

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

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?

Find effective rate (APY) and show work:

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?

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