Question 1

How long would it take for Nico to save an adequate amount for retirement if he deposits $40,000 per year into an account beginning one year from today that pays 12 percent per year if he wishes to have a total of $1,000,000 at retirement?

Accepted Answer

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Question 2

A wealthy art collector has decided to endow her favorite art museum by establishing funds for an endowment which would provide the museum with $1,000,000 per year for acquisitions into perpetuity.The art collector will give the endowment upon her fiftieth birthday 10 years from today.She plans to accumulate the endowment by making annual end-of-year deposits into an account.The rate of interest is expected to be 6 percent in all future periods.How much must the art collector deposit each year to accumulate to the required amount?

Accepted Answer

To calculate how much the art collector needs to deposit each year, we can use the formula for the future value of an annuity:

FV = PMT * ((1 + r)^n - 1) / r

where:
FV = future value of the endowment ($1,000,000 per year)
PMT = amount to be deposited each year
r = interest rate (6%)
n = number of years to accumulate the endowment (10)

Plugging in the numbers, we get:

$1,000,000 = PMT * ((1 + 0.06)^10 - 1) / 0.06

Solving for PMT, we get:

PMT = $1,264,466

Therefore, the art collector needs to deposit $1,264,466 each year to accumulate the endowment to $1,000,000 per year for acquisitions into perpetuity.

Question 3

Rita borrows $4,500 from the bank at 9 percent annually compounded interest to be repaid in three equal annual installments.The interest paid in the third year is ________.

Accepted Answer

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Question 4

Aunt Tilly borrows $3,500 from the bank at 12 percent annually compounded interest to be repaid in four equal annual installments.The interest paid in the first year is ________.

Accepted Answer

The interest paid in the first year is calculated on the initial amount borrowed. Since Aunt Tilly borrows $3,500 at 12 percent annually, the first year's interest is 12% of $3,500, which is $420.

Question 5

A local bank is offering a zero-coupon certificate of deposit for $25,000.At maturity,three years from now,the investor will receive $32,000.What is the rate of return on this investment?

Accepted Answer

To find the rate of return on this investment, we use the formula:
Rate of return = (Future value / Present value)^(1/number of years) - 1
Plugging in the given values, we get:
Rate of return = (32000 / 25000)^(1/3) - 1 
Rate of return = 0.09 or 9%
Therefore, the best choice is C, with a rate of return of 9%.

Question 6

Dorothy borrows $10,000 from the bank.For a four-year loan,the bank requires annual end-of-year payments of $3,223.73.The annual interest rate on the loan is ________.

Accepted Answer

We can use the formula for the present value of an annuity to solve for the annual interest rate:

PV = PMT * [(1 - (1 + r)^-n) / r]

where PV is the present value (the amount borrowed), PMT is the end-of-year payment amount, r is the annual interest rate, and n is the number of payments (in this case, 4).

Plugging in the given values, we get:

10,000 = 3,223.73 * [(1 - (1 + r)^-4) / r]

Solving for r using trial and error or a financial calculator yields r ≈ 0.11 or 11%. Therefore, the annual interest rate on the loan is 11%.

Question 7

Xiao Xin is planning to accumulate $40,000 by the end of 5 years by making 5 equal annual deposits.If she plans to make her first deposit today and can earn an annual compound rate of 9 percent on her investment,how much must each deposit be in order to accumulate the $40,000?

Accepted Answer

We can use the formula for the future value of an annuity, which is:
FV = PMT × ((1 + r)^n - 1) / r, where PMT is the equal annual deposit, r is the annual compound rate, and n is the number of years or deposits.
Plugging in the given values, we get:
$40,000 = PMT × ((1 + 0.09)^5 - 1) / 0.09
Solving for PMT, we get:
PMT = $6,684.08
Therefore, each deposit must be $6,684.08 in order to accumulate the $40,000.

Question 8

A local brokerage firm is offering a zero-coupon certificate of deposit for $10,000.At maturity,three years from now,the investor will receive $14,000.What is the rate of return on this investment?

Accepted Answer

The rate of return can be calculated using the formula for compound interest: $A = P(1 + r)^n$, where $A$ is the amount at maturity ($14,000), $P$ is the principal amount ($10,000), $r$ is the annual rate of return, and $n$ is the number of years (3). Rearranging the formula to solve for $r$, we get $r = \left(\frac{A}{P}\right)^{\frac{1}{n}} - 1$. Substituting the given values, we get $r = \left(\frac{14000}{10000}\right)^{\frac{1}{3}} - 1 = 1.25992 - 1 = 0.12$, or 12 percent.

Question 9

Zheng Sen wishes to accumulate $1 million by the end of 20 years by making equal annual end-of-year deposits over the next 20 years.If Zheng Sen can earn 10 percent on his investments,how much must he deposit at the end of each year?

Accepted Answer

To solve this, we use the formula for the future value of an annuity: FV = P * [((1 + r)^n - 1) / r], where FV is the future value ($1 million), P is the annual payment, r is the annual interest rate (10% or 0.10), and n is the number of periods (20 years). Rearranging the formula to solve for P gives us P = FV / [((1 + r)^n - 1) / r]. Plugging in the numbers: P = $1,000,000 / [((1 + 0.10)^20 - 1) / 0.10] = $17,460 (approximately).

Question 10

Danny Joe borrows $10,500 from the bank at 11 percent annually compounded interest to be repaid in six equal annual installments.The interest paid in the first year is ________.

Accepted Answer

The interest paid in the first year is calculated on the initial loan amount. Since the interest rate is 11 percent annually, the interest for the first year is 11% of $10,500, which is $1,155.

Question 11

Detta borrows $20,000 from the bank.For a five-year loan,the bank requires annual end-of-year payments of $4,878.05.The annual interest rate on the loan is ________.

Accepted Answer

The correct answer can be found by using the formula for the present value of an annuity, which calculates the original loan amount based on the annual payments, interest rate, and number of periods. By plugging the given values into the formula or using a financial calculator, it can be determined that an interest rate of 7 percent results in a present value (or loan amount) of $20,000 when the annual payments are $4,878.05 for five years.

Question 12

A ski chalet at Peak n' Peak now costs $250,000.Inflation is expected to cause this price to increase at 5 percent per year over the next 10 years before Chris and Julie retire from successful investment banking careers.How large an equal annual end-of-year deposit must be made into an account paying an annual rate of interest of 13 percent in order to buy the ski chalet upon retirement?

Accepted Answer

The answer of A ski chalet at Peak n' Peak...

Question 13

How long would it take for you to save an adequate amount for retirement if you deposit $40,000 per year into an account beginning today that pays 12 percent per year if you wish to have a total of $1,000,000 at retirement?

Accepted Answer

The answer of How long would it take for you...

Question 14

Uncle Butch borrows $19,500 from the bank at 8 percent annually compounded interest to be repaid in 10 equal annual installments.The interest paid in the third year is ________.

Accepted Answer

The interest paid in the third year is calculated on the remaining principal after the first two years of payments. The interest for the third year is 8% of the remaining principal at the end of the second year, which is $1,336.00.

Question 15

Otto is planning for his son's college education to begin ten years from today.He estimates the end-of-the-year tuition,books,and living expenses to be $10,000 per year for a four-year degree.How much must Otto deposit today,at an interest rate of 12 percent,for his son to be able to withdraw $10,000 per year for four years of college?

Accepted Answer

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Question 16

A beach house in Southern California now costs $350,000.Inflation is expected to cause this price to increase at 5 percent per year over the next 20 years before Eric and Karinna retire from successful careers in commercial art.How large an equal annual end-of-year deposit must be made into an account paying an annual rate of interest of 13 percent in order to buy the beach house upon retirement?

Accepted Answer

First, we need to calculate the future price of the beach house after 20 years of inflation:
Future price = $350,000 x (1 + 0.05)^20
Future price = $1,127,469.47

Next, we need to calculate the annual deposit that Eric and Karinna need to make in order to accumulate enough money for the future price of the beach house:
PV = $0 (the initial amount they have in the account)
FV = $1,127,469.47
n = 20
i = 0.13

Using the formula for annuity payment:
PMT = (FV x i) / [(1 + i)^n - 1]
PMT = ($1,127,469.47 x 0.13) / [(1 + 0.13)^20 - 1]
PMT = $11,472.11

Therefore, Eric and Karinna need to make an equal annual end-of-year deposit of $11,472.11 in order to buy the beach house upon retirement. Answer choice A is correct.

Question 17

How many years would it take for Harry to save an adequate amount for retirement if he deposits $2,000 per month into an account beginning today that pays 12 percent per year if he wishes to have a total of $1,000,000 at retirement?

Accepted Answer

We can use the formula for future value of an annuity to calculate the number of years it would take for Harry to save $1,000,000:

FV = P * (((1 + r)^n - 1) / r)

where FV is the future value, P is the monthly deposit, r is the annual interest rate divided by 12, and n is the number of months.

Substituting in the given values, we get:

$1,000,000 = $2,000 * (((1 + 0.12/12)^n - 1) / (0.12/12))

Simplifying this equation, we can solve for n:

n = log(1 + ($1,000,000 / $2,000) * (0.12/12)) / log(1 + 0.12/12)

n ≈ 180.81

Therefore, it would take approximately 15 years for Harry to save $1,000,000 for retirement. The closest answer choice is C.

Question 18

Entertainer's Aid plans five annual colossal concerts,each in a different nation's capital.The concerts will raise funds for an endowment which would provide the World Wide Hunger Fund with $3,000,000 per year into perpetuity.The endowment will be given at the end of the fifth year.The rate of interest is expected to be 9 percent in all future periods.How much must Entertainer's Aid deposit each year to accumulate to the required amount?

Accepted Answer

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Question 19

Thelma is planning for her son's college education to begin five years from today.She estimates the yearly tuition,books,and living expenses to be $5,000 per year for a four-year degree,assuming the expenses incur only at the end of the year.How much must Thelma deposit today,at an interest rate of 8 percent,for her son to be able to withdraw $5,000 per year for four years of college?

Accepted Answer

Thelma needs to calculate the present value of an annuity of $5,000 per year for four years at an 8% interest rate. The present value of this annuity is then discounted back five years to find the amount she needs to deposit today.

Question 20

Xiao Li wishes to accumulate $50,000 by the end of 10 years by making equal annual end-of-year deposits over the next 10 years.If Xiao Li can earn 5 percent on her investments,how much must she deposit at the end of each year?

Accepted Answer

The answer of Xiao Li wishes to accumulate $50,000 by...

Quiz 5: Time Value of Money