Question 1

Margaret Bodner opened a savings account for her new-born niece with $2,000. The
account pays 4% interest a year. How much will the account have in it when her niece
turns 20?

Accepted Answer

The answer of Margaret Bodner opened a savings account for...

Question 2

Suppose you deposit $1,000 today in an account that pays interest at an annual rate of 5%. What will be the balance in the account at the end of two years if you withdraw only the
Interest paid on the interest at that time?

Accepted Answer

The answer of Suppose you deposit $1,000 today in an...

Question 3

If interest is compounded daily, then

Accepted Answer

When interest is compounded daily, the compounding frequency is higher than if interest were compounded monthly. As a result, the effective annual rate (AER) will be higher than the annual percentage rate (APR). Therefore, option C is correct. When interest is compounded daily, the effective annual rate (AER) is higher than the annual percentage rate (APR). This is because with daily compounding, interest is being earned on the principal amount plus any previously earned interest every single day, resulting in greater overall earnings. As a result, the APR will be lower than the AER when interest is compounded daily.

Question 4

If you deposit $20,000 today in a bank account at a quoted rate of 12%, compounded quarterly, how much will be in the account in five years if you make no withdrawals? Round your
Answer to the nearest dollar.

Accepted Answer

We can use the formula A=P(1+r/n)^(nt), where A is the amount, P is the principal, 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.
Plugging in the given values, we get:
A = 20000(1+0.12/4)^(4*5)
A = 36122.08
Rounding to the nearest dollar, we get $36,122. Therefore, the best answer choice is A.

Question 5

A gallon of gasoline cost $0.39 during the summer of 1968 and $3.50 in the summer of 2008. To the nearest tenth of a percent, this is an average annual increase of

Accepted Answer

The average annual increase can be calculated using the formula for compound annual growth rate (CAGR), which is $$CAGR = \left( \frac{FV}{PV} \right)^{\frac{1}{n}} - 1$$, where FV is the final value ($3.50), PV is the initial value ($0.39), and n is the number of years (2008 - 1968 = 40 years). Plugging these values in gives $$CAGR = \left( \frac{3.50}{0.39} \right)^{\frac{1}{40}} - 1 \approx 0.056$$ or 5.6% when converted to a percentage.

Question 6

A mutual fund reported the following quarterly returns: 2%, -5%, 4%, 1%. To the nearest tenth of a percent, this represents an annual return of

Accepted Answer

To find the annual return, we need to compound the quarterly returns. One way to do this is to use the following formula:

(1 + r1)(1 + r2)(1 + r3)(1 + r4) - 1

where r1 through r4 are the quarterly returns as decimals. Applying this formula to the given returns yields:

(1 + 0.02)(1 - 0.05)(1 + 0.04)(1 + 0.01) - 1 = 0.018

Multiplying by 100 to convert to a percentage gives 1.8%. Therefore, the best choice is B.

Question 7

The Monumental Returns Investment Company is offering you an investment that promises you $1,000 at the end of ten years if you invest $500 today. What average annual rate of return
Does this investment promise? Round your answer to the nearest tenth of a percent.

Accepted Answer

We can use the formula for compound interest:

A = P(1+r)^n

Where A is the future value, P is the present value, r is the annual interest rate as a decimal, and n is the number of years.

Plugging in the values given, we have:

1000 = 500(1+r)^10

Dividing both sides by 500:

2 = (1+r)^10

Taking the tenth root of both sides:

1.072 = 1+r

Subtracting 1 from both sides:

r = 0.072 or 7.2%

Therefore, the investment promises an average annual rate of return of 7.2%. The best choice is D.

Question 8

How long will it take for a $1,000 investment to grow to $3,000 if the interest rate per year is 8%, and interest is paid only at the end of each year?

Accepted Answer

To find out how long it will take for a $1,000 investment to grow to $3,000 with an annual interest rate of 8%, we can use the formula for compound interest, which is A = P(1 + r)^t, where A is the amount of money accumulated after n years, including interest, P is the principal amount ($1,000), r is the annual interest rate (8% or 0.08), and t is the time the money is invested for in years. We need to solve for t when A is $3,000, P is $1,000, and r is 0.08.$3,000 = $1,000(1 + 0.08)^t3 = (1.08)^tTo solve for t, we take the logarithm of both sides:log(3) = t * log(1.08)t = log(3) / log(1.08)t ≈ 14.897Since t represents the number of years and it must be a whole number, we round up to the nearest whole year, which gives us 15 years.

Question 9

If you deposit $20,000 today in an account at a quoted rate of 16% a year, compounded semiannually, how much will you have in the account at the end of five years if you make no
Withdrawals?

Accepted Answer

The answer of If you deposit $20,000 today in an...

Question 10

An investment earned 12% in one year. This represents an average monthly return of

Accepted Answer

To calculate the average monthly return, we divide the annual return by 12 (the number of months in a year): 
Average monthly return = 12% / 12 = 1%. 
One basis point is equal to 0.01%, so 1% is equal to 100 basis points. Therefore, the average monthly return is 100 basis points x 1% = 100 basis points. 
Therefore, the correct answer is B) 95 basis points, as it is the closest option to 100 basis points. To find the average monthly return, we need to divide the annual return by 12 (the number of months in a year).

12% / 12 = 1%

1% is equivalent to 100 basis points. Therefore, the answer cannot be A or D.

9 basis points is much lower than 1%, so the answer cannot be C.

The closest answer is B, which is 95 basis points. This makes sense because 1% is equivalent to 100 basis points, so 12% is equivalent to 1200 basis points.

1200 basis points / 12 months = 100 basis points per month

However, it's worth noting that "average monthly return" can be interpreted different ways (e.g. arithmetic mean vs. geometric mean), so the answer may vary depending on the context of the question.

Question 11

How long will it take to triple your investment if the interest rate per year is 9%, and interest is paid only at the end of each year?

Accepted Answer

The rule of 72 is a simple way to estimate the number of years required to double the investment at a given annual rate of return. By dividing 72 by the annual rate of return, investors can get a rough estimate of how many years it will take for the initial investment to duplicate itself. In this case, to triple an investment at a 9% interest rate, we can modify the rule slightly. Doubling the investment would take approximately 72 / 9 = 8 years. Tripling would take longer, but since only one option is close to being reasonable given the exponential growth nature of compound interest, 13 years is the best estimate without doing the exact calculation. The exact calculation involves using the formula for compound interest, but given the options and the nature of the question, a detailed calculation isn't necessary to select the most reasonable answer.

Question 12

If you had deposited $1.00 in a bank account at an annual rate of 2% at the beginning of 1929, how much would you have in the account at the end of 2008, assuming the interest rate
Remained constant?

Accepted Answer

The answer of If you had deposited $1.00 in a...

Question 13

If $100 is deposited into an account that earns a quoted rate of 16%, compounded quarterly, for five years, how much will be in the account at the end of the 5th year? Round your answer to
The nearest dollar.

Accepted Answer

The amount in the account at the end of the 5th year 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 (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. Here, P = $100, r = 16% or 0.16, n = 4 (since the interest is compounded quarterly), and t = 5 years. Plugging these values into the formula gives A = 100(1 + 0.16/4)^(4*5) = 100(1 + 0.04)^20 ≈ $219.

Question 14

You invested $1,000 in a mutual fund at the beginning of the year. The fund reported the following quarterly returns during the year: -5%, 5%, 4%, and 8%. How much will you have
In your account at the end of the year, assuming you made no additional deposits or
Withdrawals? Ignore any fees and round your answer to the nearest dollar.

Accepted Answer

First, we need to calculate the quarterly returns using the formula: 
Quarterly return = (ending value - beginning value) / beginning value

For the first quarter: 
Quarterly return = (-5% / 100) * $1,000 = -$50

For the second quarter: 
Quarterly return = (5% / 100) * ($1,000 - $50) = $47.50

For the third quarter: 
Quarterly return = (4% / 100) * ($1,000 + $47.50) = $48.70

For the fourth quarter: 
Quarterly return = (8% / 100) * ($1,000 + $47.50 + $48.70) = $100.78

Now, we can calculate the ending value of the investment: 
Ending value = $1,000 - $50 + $47.50 + $48.70 + $100.78 = $1,146.98

Rounding to the nearest dollar, we get $1,120. Therefore, the answer is C. To find the balance at the end of the year, we need to apply each quarterly return sequentially to the initial investment of $1,000:
First quarter: -5% return on $1,000 equals a balance of $950.
Second quarter: 5% return on $950 equals a balance of $997.50.
Third quarter: 4% return on $997.50 equals a balance of $1,036.50.
Fourth quarter: 8% return on $1,036.50 equals a balance of $1,120.02.
Rounding to the nearest dollar gives us an account balance of $1,120, which is option C.

Question 15

If you deposit $1,000 today in a bank account that pays 4%, compounded quarterly, how much will you have in ten years?

Accepted Answer

Use the formula:

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

where:

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

Plugging in the values given in the problem, we get:

A = 1000(1 + 0.04/4)^(4*10)
A = 1000(1 + 0.01)^40
A = 1000(1.01)^40
A = 1000(1.4889)

A = $1,488.86

Therefore, the best choice is (D) $1,488.86. We can use the formula A=P(1+r/n)^(nt) where:
A = the amount after time t,
P = the principal (initial amount),
r = the annual interest rate (as a decimal),
n = the number of times the interest is compounded per year, and
t = the time in years.

Plugging in the values, we get:

A = 1000(1+0.04/4)^(4*10)
A = 1000(1.01)^40
A = 1000(1.48024)
A = $1488.86

Therefore, the answer is D.

Question 16

Suppose you deposit $1,000 today in an account that pays 5% interest at the end of each year. If you withdraw one half of the year's interest at the end of each year, what is the balance in
Your account after your third withdrawal? Round your answer to the nearest dollar.

Accepted Answer

After one year: 
Balance = $1,000 + 5% of $1,000 = $1,050 
Withdrawal = 1/2 * 5% of $1,000 = $25 
Remaining balance= $1,025

After the second year: 
Balance = $1,025 + 5% of $1,025 = $1,076.25 
Withdrawal = 1/2 * 5% of $1,025 = $25.62.5 
Remaining balance= $1,050.63

After the third year: 
Balance = $1,050.63 + 5% of $1,050.63 = $1,103.16 
Withdrawal = 1/2 * 5% of $1,050.63 = $26.27 
Remaining balance= $1,076.89

Rounding to the nearest dollar gives a balance of $1,077. Therefore, the best choice is B. After one year, the interest earned is $1,000 x 0.05 = $50. If you withdraw half of this, you take out $25, leaving your balance at the end of year one at $1,025.

After two years, the interest earned is $1,025 x 0.05 = $51.25. If you withdraw half of this, you take out $25.63, leaving your balance at the end of year two at $1,051.63.

After three years, the interest earned is $1,051.63 x 0.05 = $52.58. If you withdraw half of this, you take out $26.29, leaving your balance at the end of year three at $1,077.29. Therefore, the best choice is B, with the balance being $1,077.

Question 17

In which of the following accounts would you prefer to invest your money?

Accepted Answer

The account that pays 4.75% compounded quarterly offers the highest interest rate with a compounding frequency that is more frequent than annual but less so than daily or monthly, balancing a high rate with beneficial compounding effects.

Question 18

Sam refuses to retire until his retirement account has a balance of at least $1 million. The account currently has a balance of $500,000, and earns a rate of 9%, compounded monthly. If
Sam does not plan to make any more deposits into his account, how long will he have to wait
Until he retires?

Accepted Answer

The answer of Sam refuses to retire until his retirement...

Question 19

The TriValley Corporation has a 3-month loan of $30,000. At the end of three months, the firm must repay the $30,000 plus $675 in interest. What is the effective annual rate on this loan?

Accepted Answer

The answer of The TriValley Corporation has a 3-month loan...

Question 20

Which of the following loan terms would result in the lowest annual cost?

Accepted Answer

The loan term with the lowest annual cost is the one with the lowest effective annual interest rate (APY). The effective annual interest rate is calculated as (1 + (nominal rate/number of times compounded per year))^number of times compounded per year - 1. Therefore, for a 4% nominal rate, the effective annual interest rate would be:

A) (1 + (4%/1))^1 - 1 = 4.00%
B) (1 + (4%/12))^12 - 1 = 4.07%
C) (1 + (4%/4))^4 - 1 = 4.08%
D) (1 + (4%/365))^365 - 1 = 4.09%

As we can see, option A has the lowest effective annual interest rate and therefore results in the lowest annual cost. The loan with the lower compounding frequency will result in a lower annual cost. Since option A is compounded annually, it will have the lowest annual cost.

Quiz 2: The Time Value of Money and Net Present Value

Margaret Bodner opened a savings account for her new-born niece with $2,000. The account pays 4% interest a year. How much will the account have in it when her niece turns 20?

Suppose you deposit $1,000 today in an account that pays interest at an annual rate of 5%. What will be the balance in the account at the end of two years if you withdraw only the Interest paid on the interest at that time?

If interest is compounded daily, then

If you deposit $20,000 today in a bank account at a quoted rate of 12%, compounded quarterly, how much will be in the account in five years if you make no withdrawals? Round your Answer to the nearest dollar.

A gallon of gasoline cost $0.39 during the summer of 1968 and $3.50 in the summer of 2008. To the nearest tenth of a percent, this is an average annual increase of

A mutual fund reported the following quarterly returns: 2%, -5%, 4%, 1%. To the nearest tenth of a percent, this represents an annual return of

The Monumental Returns Investment Company is offering you an investment that promises you $1,000 at the end of ten years if you invest $500 today. What average annual rate of return Does this investment promise? Round your answer to the nearest tenth of a percent.

How long will it take for a $1,000 investment to grow to $3,000 if the interest rate per year is 8%, and interest is paid only at the end of each year?

If you deposit $20,000 today in an account at a quoted rate of 16% a year, compounded semiannually, how much will you have in the account at the end of five years if you make no Withdrawals?

An investment earned 12% in one year. This represents an average monthly return of

How long will it take to triple your investment if the interest rate per year is 9%, and interest is paid only at the end of each year?

If you had deposited $1.00 in a bank account at an annual rate of 2% at the beginning of 1929, how much would you have in the account at the end of 2008, assuming the interest rate Remained constant?

If $100 is deposited into an account that earns a quoted rate of 16%, compounded quarterly, for five years, how much will be in the account at the end of the 5th year? Round your answer to The nearest dollar.

If you deposit $1,000 today in a bank account that pays 4%, compounded quarterly, how much will you have in ten years?

Suppose you deposit $1,000 today in an account that pays 5% interest at the end of each year. If you withdraw one half of the year's interest at the end of each year, what is the balance in Your account after your third withdrawal? Round your answer to the nearest dollar.

In which of the following accounts would you prefer to invest your money?

Sam refuses to retire until his retirement account has a balance of at least $1 million. The account currently has a balance of $500,000, and earns a rate of 9%, compounded monthly. If Sam does not plan to make any more deposits into his account, how long will he have to wait Until he retires?

The TriValley Corporation has a 3-month loan of $30,000. At the end of three months, the firm must repay the $30,000 plus $675 in interest. What is the effective annual rate on this loan?

Which of the following loan terms would result in the lowest annual cost?