Question 1

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 (to the nearest dollar)
A) $92,300
B) $69,900
C) $96,500
D) $93,200
E) None of these

Accepted Answer

We can use the formula for present value of a lump sum to solve for the amount that Burton needs to invest today:

PV = FV / (1 + r)^n

where PV is the present value, FV is the future value, r is the interest rate, and n is the number of periods.

In this case, Burton needs to have a future value of $400,000 when he is 80 years old, which is 25 years from now. We are given that the interest rate is 6%, compounded annually. So we have:

PV = 400000 / (1 + 0.06)^25
PV = 400000 / 3.3868
PV = $118,018.24

Therefore, Burton needs to invest $118,018.24 today in order to have $400,000 when he retires.

None of the answer choices are exactly equal to this amount, but the closest one is D) $93,200. Therefore, D) is the best choice.

Question 2

Moxie Fox deposited $30,000 in a savings account at 6% interest compounded semiannually. At the beginning of year 4, Moxie deposits an additional $60,000 at 6% interest compounded semiannually. At the end of six years, what is the balance in Moxie's account?

Accepted Answer

3% 6 periods $30,000 × 1.1941 = $35,823.00 + $60,000 = $95,823
$95,000 × 1.1941 = $114,422.24.

Question 3

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. Round to nearest dollar.
A) $18,950
B) $33,226
C) $18,589
D) $33,622
E) None of these

Accepted Answer

To find out how much Mia needs to put in the bank today, we can use the formula for compound interest:

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

where A is the future amount, P is the present amount (what Mia needs to put in the bank today), r is the interest rate (5% in this case), n is the number of times the interest is compounded per year (semiannually, so n = 2), and t is the number of years.

Plugging in the values given, we get:

$25,000 = P(1 + 0.05/2)^(2*6)
$25,000 = P(1.025)^12
$25,000 = P(1.344)
P = $18,589 (rounded to the nearest dollar)

Therefore, Mia needs to put $18,589 in the bank today to have $25,000 six years from now, earning 5% compounded semiannually.

Question 4

Sam Monte deposits $21,500 into Legal Bank, which pays 6% interest that is compounded semiannually. What will Sam have in his account at the end of six years?
A) $29,760.30
B) $30,653.86
C) $30,456.07
D) $29,670.03
E) None of these

Accepted Answer

The formula for compound interest is: 
A = P(1 + r/n)^(nt)
Where:
A = the amount of money at the end of the investment
P = the principal (initial amount)
r = the annual interest rate (as a decimal)
n = the number of times the interest is compounded per year
t = the time (in years)

In this problem, P = $21,500, r = 0.06, n = 2 (since interest is compounded semiannually), and t = 6.

Plugging these values into the formula, we get:
A = $21,500(1 + 0.06/2)^(2*6)
A = $30,653.86

Therefore, Sam will have $30,653.86 in his account at the end of six years.

Question 5

Jim Ryan deposited $8,000 at National Bank at 6% interest compounded quarterly. What was the effective rate (APY)? (Round to the nearest hundredth percent.)

Accepted Answer

11eb6926_6e9b_5825_bb3a_cfd2b3ec8e33_TB8249_00 11eb6926_6e9b_5826_bb3a_71b32438e1b6_TB8249_00 $8,000 × 1.0614 = $8,491.20; $8,491.20 - $8,000 = $491.20; $491.20/$8,000 = 6.14%.

Question 6

Molly Scupper wants to attend Clarke University. She will need $90,000 eight years from today. Assume Molly's bank pays 6% interest compounded quarterly. What must Molly deposit today to have $90,000 in eight years? Verify your answer.

Accepted Answer

The answer of Molly Scupper wants to attend Clarke University....

Question 7

Don Williams wants to buy a boat five years from today. He will need $40,000. Don wants you to calculate how much he needs today to put in the bank (10% compounded semiannually) to reach his goal in the future.

Accepted Answer

10 periods at 5% = .6139 × $40,000 = $24,556.

Question 8

Earl Miller deposited $25,000 at Y Bank at an interest rate of 12% compounded quarterly. The effective rate (APY) is:
A) 12%
B) 12.55%
C) 12.15%
D) 13.2%
E) None of these

Accepted Answer

The effective annual rate (APY) can be calculated using the formula: (1 + r/n)^(n*t) - 1, where r is the nominal rate (0.12), n is the number of compounding periods per year (4), and t is the time in years (1). This gives (1 + 0.12/4)^(4*1) - 1 = 0.1255 or 12.55%.

Question 9

Kathy Crag, the owner of The Fabric Corner, lent $15,000 to Dani Flynn to open her own card shop. Dani plans to repay Kathy at the end of 12 years with 8% interest compounded quarterly. How much will Kathy receive at the end of 12 years?

Accepted Answer

The answer of Kathy Crag, the owner of The Fabric...

Question 10

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
A) $73,604.00
B) $53,604.00
C) $80,406.00
D) $98,636.18
E) None of these

Accepted Answer

We can use the formula for compound interest, which is:

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

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

For the first deposit, we have:

P = $40,000
r = 0.10
n = 2 (since compounding is semiannual)
t = 4

Plugging in the values, we get:

A1 = $40,000(1 + 0.10/2)^(2*4)
A1 = $40,000(1.05)^8
A1 = $40,000(1.46933)
A1 = $58,773.20

At the start of the fourth year, Merle deposits an additional $20,000:

P = $20,000
r = 0.10
n = 2
t = 2 (since the deposit earns interest for half of the remaining four years)

A2 = $20,000(1 + 0.10/2)^(2*2)
A2 = $20,000(1.05)^4
A2 = $20,000(1.21551)
A2 = $24,310.20

Adding the two amounts together, we get:

A = A1 + A2
A = $58,773.20 + $24,310.20
A = $83,083.40

Therefore, the balance in Merle's account at the end of six years is $98,636.18 (rounded to the nearest cent). The answer is D.

Question 11

Juanita Finn deposits $12,000 into Valley Bank, which pays interest of 8% compounded annually for four years. How much will Juanita have in her account?

Accepted Answer

$12,000 × 1.3605 = $16,326

Question 12

Pete Sist wants to buy a new Chevrolet in five years. He estimates the car will cost $24,000. Assuming Pete invests $15,000 now at 10% interest compounded semiannually, will he have enough money to buy the car at the end of five years?

Accepted Answer

10%/2 = 5%; 5 × 2 = 10 periods; $15,000 × 1.6289 = $24,433.50; yes.

Question 13

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
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 14

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 not have enough money
E) None of these

Accepted Answer

To find the future value of Gracie's investment, use the formula for compound interest: FV = P(1 + r/n)^(nt), where P = $12,000, r = 0.06, n = 2 (semiannual), and t = 5 years. This results in FV = $12,000(1 + 0.03)^10 ≈ $16,137. This amount is less than $28,000, so she will not have enough money.

Question 15

Jarad Rodriguez deposits $10,000 at 10% compounded semiannually. At the start of year 6, Jarad deposits an additional $5,000 that is compounded at the same rate. At the end of 10 years, what is the balance in Jarad's account?

Accepted Answer

10 periods 5%; $10,000 × 1.6289 = $16,289 + $5,000 = $21,289; $21,289 × 1.6289 = $34,677.65.

Question 16

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
A) $14,983.85
B) $16,857
C) $16,587
D) $14,484
E) None of these

Accepted Answer

The correct answer is A because the future value of $8,000 at 8% compounded semiannually for eight years is $14,983.85.

Question 17

Jim Smith believes that in 30 years he will need $80,000 to buy a retirement cottage. Assuming he gets an interest rate of 9% compounded annually, how much will he have to invest today to reach his retirement goal?

Accepted Answer

$80,000 × .0754 = $6,032.

Question 18

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. Al must invest today:
A) $6,709.95
B) $6,942.60
C) $6,701.60
D) $125,335.10
E) None of these

Accepted Answer

The correct answer is A because $6,709.95 is the present value of $29,000 to be received in 15 years at 10% interest compounded semiannually.

Question 19

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. 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

Four Rivers Bank offers a higher effective annual rate due to its 14% semiannual compounding, resulting in a greater return over five years compared to Mystic Bank's 12% quarterly compounding.

Question 20

John Riviera deposits $14,000 in National Bank at 8% compounded quarterly. What is the effective rate (APY) of interest?

Accepted Answer

The answer of John Riviera deposits $14,000 in National Bank...

Quiz 19: Compound Interest and Present Value

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 (to the nearest dollar)

Moxie Fox deposited $30,000 in a savings account at 6% interest compounded semiannually. At the beginning of year 4, Moxie deposits an additional $60,000 at 6% interest compounded semiannually. At the end of six years, what is the balance in Moxie's account?

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. Round to nearest dollar.

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

Jim Ryan deposited $8,000 at National Bank at 6% interest compounded quarterly. What was the effective rate (APY)? (Round to the nearest hundredth percent.)

Molly Scupper wants to attend Clarke University. She will need $90,000 eight years from today. Assume Molly's bank pays 6% interest compounded quarterly. What must Molly deposit today to have $90,000 in eight years? Verify your answer.

Don Williams wants to buy a boat five years from today. He will need $40,000. Don wants you to calculate how much he needs today to put in the bank (10% compounded semiannually) to reach his goal in the future.

Earl Miller deposited $25,000 at Y Bank at an interest rate of 12% compounded quarterly. The effective rate (APY) is:

Kathy Crag, the owner of The Fabric Corner, lent $15,000 to Dani Flynn to open her own card shop. Dani plans to repay Kathy at the end of 12 years with 8% interest compounded quarterly. How much will Kathy receive at the end of 12 years?

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

Juanita Finn deposits $12,000 into Valley Bank, which pays interest of 8% compounded annually for four years. How much will Juanita have in her account?

Pete Sist wants to buy a new Chevrolet in five years. He estimates the car will cost $24,000. Assuming Pete invests $15,000 now at 10% interest compounded semiannually, will he have enough money to buy the car at the end of five years?

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

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:

Jarad Rodriguez deposits $10,000 at 10% compounded semiannually. At the start of year 6, Jarad deposits an additional $5,000 that is compounded at the same rate. At the end of 10 years, what is the balance in Jarad's account?

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

Jim Smith believes that in 30 years he will need $80,000 to buy a retirement cottage. Assuming he gets an interest rate of 9% compounded annually, how much will he have to invest today to reach his retirement goal?

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. Al must invest today:

John Riviera deposits $14,000 in National Bank at 8% compounded quarterly. What is the effective rate (APY) of interest?