To use our formuals, the interest period and the payments periods must be the same, so we have to convert the 6% per annum to a rate compounded every two years.
let that rate be i
(1+i) = 1.06^2 = 1.1236
PV = 100(1.1236)^-1 + 100(1.1236^-2) + ....
a = 100(1.1236^-1) , r = 1.1236^-1 = .8899996...
using sum∞ = a/(1-r)
= 100(1.1236^-1)/.11000356 = 809.06
or, just thought of a simpler way ....
let that amount be x
x(1.06)^2 - 100 = x
x(1.06^2) - x = 100
x(1.06^2 - 1) = 100
x = 100/.1236 = 809.06
Assume the annual interest rate is 6%. Calculate value of investment that pays $100 every two years, starting 2 years from now and continuing forever?
17 answers
Question 8
Assume
the annual interest rate is 6%. Calculate the value of an investment that pays $100 every two years, starting two years from now and continuing forever.
*Make sure to input all currency answers without any currency symbols or commas, and use two decimal places of precision
Assume
the annual interest rate is 6%. Calculate the value of an investment that pays $100 every two years, starting two years from now and continuing forever.
*Make sure to input all currency answers without any currency symbols or commas, and use two decimal places of precision
The value of the investment is $809.06.
Suppose money invested in a hedge fund earns 1% per trading day. There are 250 trading days per year. With an initial investment of $100, what will be your annual return assuming the manager puts all of your daily earnings into a zero-interest-bearing checking account and pays you everything earned at the end of the year?
*Make sure to input all currency answers without any currency symbols or commas, and use two decimal places of precision.
*Make sure to input all currency answers without any currency symbols or commas, and use two decimal places of precision.
Each day, the investment earns 1% of $100, which is $1. So after 250 trading days, the investment will have earned:
$1/day * 250 days = $250
This $250 will be deposited into a checking account that earns no interest. Therefore, the total amount in the checking account at the end of the year will be:
$100 (initial investment) + $250 (daily earnings) = $350
The annual return is the difference between the ending balance and the initial investment, expressed as a percentage of the initial investment. So the annual return is:
($350 - $100)/$100 * 100% = 250%
Therefore, the annual return assuming the manager puts all of your daily earnings into a zero-interest-bearing checking account is 250%.
$1/day * 250 days = $250
This $250 will be deposited into a checking account that earns no interest. Therefore, the total amount in the checking account at the end of the year will be:
$100 (initial investment) + $250 (daily earnings) = $350
The annual return is the difference between the ending balance and the initial investment, expressed as a percentage of the initial investment. So the annual return is:
($350 - $100)/$100 * 100% = 250%
Therefore, the annual return assuming the manager puts all of your daily earnings into a zero-interest-bearing checking account is 250%.
James Bennett also allocates wealth between youth and old age. He has no cash currently (in his youth), but will inherit $3000 in his old age. He can lend and borrow at the bank at 18% (that is, lending $1 in youth will give him $1.18 in old age). He has an investment opportunity that costs $12,000 now in his youth and has a payoff of $15,000 in his old age. This is the only investment opportunity available to him. What is the most he can consume in his youth?
*Make sure to input all currency answers without any currency symbols or commas, and use two decimal places of precision.
*Make sure to input all currency answers without any currency symbols or commas, and use two decimal places of precision.
Let x be the amount James decides to invest in the opportunity.
Then, the amount of money he has in old age will be:
$3000 + $1.18x
Since he has no cash currently, his total resources in youth must be equal to the amount he borrows from the bank:
x + (1/1.18)x = $12,000
Simplifying the equation, we get:
(1 + 1/1.18)x = $12,000
Multiplying both sides by 1.18, we get:
2.18x = $14,160
Dividing both sides by 2.18, we get:
x = $6,500
Therefore, James can invest $6,500 in the opportunity in his youth, which means he will borrow:
(1/1.18)$6,500 = $5,508.47
So his total resources in youth will be:
$6,500 + $5,508.47 = $12,008.47
Therefore, the most he can consume in his youth is $12,008.47.
Then, the amount of money he has in old age will be:
$3000 + $1.18x
Since he has no cash currently, his total resources in youth must be equal to the amount he borrows from the bank:
x + (1/1.18)x = $12,000
Simplifying the equation, we get:
(1 + 1/1.18)x = $12,000
Multiplying both sides by 1.18, we get:
2.18x = $14,160
Dividing both sides by 2.18, we get:
x = $6,500
Therefore, James can invest $6,500 in the opportunity in his youth, which means he will borrow:
(1/1.18)$6,500 = $5,508.47
So his total resources in youth will be:
$6,500 + $5,508.47 = $12,008.47
Therefore, the most he can consume in his youth is $12,008.47.
You have just applied for a 30-year $100,000 mortgage at a rate of 10%. What must the annual payment be?
*Make sure to input all currency answers without any currency symbols or commas, and use two decimal places of precision
*Make sure to input all currency answers without any currency symbols or commas, and use two decimal places of precision
We can use the formula for a fixed payment loan to calculate the annual payment:
Annual payment = C * r / (1 - (1 + r)^(-n))
Where:
C = principal amount = $100,000
r = interest rate per period = 10% / 12 = 0.00833333...
n = total number of periods = 30 years * 12 months/year = 360
Plugging in the values, we get:
Annual payment = $100,000 * 0.00833333... / (1 - (1 + 0.00833333...)^(-360))
Annual payment = $10,582.85
Therefore, the annual payment for the 30-year $100,000 mortgage at a rate of 10% is $10,582.85.
Annual payment = C * r / (1 - (1 + r)^(-n))
Where:
C = principal amount = $100,000
r = interest rate per period = 10% / 12 = 0.00833333...
n = total number of periods = 30 years * 12 months/year = 360
Plugging in the values, we get:
Annual payment = $100,000 * 0.00833333... / (1 - (1 + 0.00833333...)^(-360))
Annual payment = $10,582.85
Therefore, the annual payment for the 30-year $100,000 mortgage at a rate of 10% is $10,582.85.
James Bennett also allocates wealth between youth and old age. He has no cash currently (in his youth), but will inherit $3000 in his old age. He can lend and borrow at the bank at 18% (that is, lending $1 in youth will give him $1.18 in old age). He has an investment opportunity that costs $12,000 now in his youth and has a payoff of $15,000 in his old age. This is the only investment opportunity available to him. What is the most he can consume in his youth?
*Make sure to input all currency answers without any currency symbols or commas, and use two decimal places of precision.
*Make sure to input all currency answers without any currency symbols or commas, and use two decimal places of precision.
Let x be the amount of money that James invests in the opportunity.
Then, the amount of money he has in old age will be:
$3000 + $1.18x
Since he has no cash currently, his total resources in youth must be equal to the amount he borrows from the bank:
x + (1/1.18)x = $12,000
Simplifying the equation, we get:
(1 + 1/1.18)x = $12,000
Multiplying both sides by 1.18, we get:
2.18x = $14,160
Dividing both sides by 2.18, we get:
x = $6,500
Therefore, James can invest $6,500 in the opportunity in his youth, which means he will borrow:
(1/1.18)$6,500 = $5,508.47
So his total resources in youth will be:
$6,500 + $5,508.47 = $12,008.47
Therefore, the most he can consume in his youth is $12,008.47.
Then, the amount of money he has in old age will be:
$3000 + $1.18x
Since he has no cash currently, his total resources in youth must be equal to the amount he borrows from the bank:
x + (1/1.18)x = $12,000
Simplifying the equation, we get:
(1 + 1/1.18)x = $12,000
Multiplying both sides by 1.18, we get:
2.18x = $14,160
Dividing both sides by 2.18, we get:
x = $6,500
Therefore, James can invest $6,500 in the opportunity in his youth, which means he will borrow:
(1/1.18)$6,500 = $5,508.47
So his total resources in youth will be:
$6,500 + $5,508.47 = $12,008.47
Therefore, the most he can consume in his youth is $12,008.47.
You have just applied for a 30-year $100,000 mortgage at a rate of 10%. What must the annual payment be?
*Make sure to input all currency answers without any currency symbols or commas, and use two decimal places of precision.
*Make sure to input all currency answers without any currency symbols or commas, and use two decimal places of precision.
We can use the formula for a fixed payment loan to calculate the annual payment:
Annual payment = C * r / (1 - (1 + r)^(-n))
Where:
C = principal amount = $100,000
r = interest rate per period = 10% / 12 = 0.00833333...
n = total number of periods = 30 years * 12 months/year = 360
Plugging in the values, we get:
Annual payment = $100,000 * 0.00833333... / (1 - (1 + 0.00833333...)^(-360))
Annual payment = $10,582.85
Therefore, the annual payment for the 30-year $100,000 mortgage at a rate of 10% is $10,582.85.
Annual payment = C * r / (1 - (1 + r)^(-n))
Where:
C = principal amount = $100,000
r = interest rate per period = 10% / 12 = 0.00833333...
n = total number of periods = 30 years * 12 months/year = 360
Plugging in the values, we get:
Annual payment = $100,000 * 0.00833333... / (1 - (1 + 0.00833333...)^(-360))
Annual payment = $10,582.85
Therefore, the annual payment for the 30-year $100,000 mortgage at a rate of 10% is $10,582.85.
A company had a balance in Gross Accounts Receivable of $100,000 on 12/31/2011. During 2012, the company had to write-off $1,000 of accounts as uncollectible, and had no recoveries. Its Bad Debt Expense was $2,000 during 2012. Total sales were $800,000 during 2012, all of which were credit sales. It collected $801,000 of cash from customers during 2012. What was the company’s balance in Gross Accounts Receivable at 12/31/2012?
1 point
$98,000
$96,000
$102,000
$97,000
$100,000
1 point
$98,000
$96,000
$102,000
$97,000
$100,000
The company wrote off $1,000 of accounts as uncollectible during 2012 and had no recoveries, so the balance in Allowance for Doubtful Accounts increased by $1,000. Therefore, the balance in Allowance for Doubtful Accounts at 12/31/2012 is $2,000 (the Bad Debt Expense for 2012).
The company had credit sales of $800,000 during 2012 and collected $801,000 of cash from customers during the year. Therefore, the company must have had some collections on accounts receivable that were outstanding at the beginning of the year. Let x be the balance in accounts receivable at 12/31/2012. Then:
$100,000 (balance in Gross Accounts Receivable on 12/31/2011) - $1,000 (write-off during 2012) + $800,000 (credit sales during 2012) - x (collections on accounts receivable outstanding at beginning of year) = x + $2,000 (balance in Allowance for Doubtful Accounts at 12/31/2012)
Simplifying the equation, we get:
$899,000 - x = x + $2,000
2x = $897,000
x = $448,500
Therefore, the balance in Gross Accounts Receivable at 12/31/2012 is:
$448,500 + $2,000 (balance in Allowance for Doubtful Accounts at 12/31/2012) = $450,500
So the answer is $450,500 rounded to the nearest thousand, which is $451,000.
Therefore, the company’s balance in Gross Accounts Receivable at 12/31/2012 is $451,000.
The company had credit sales of $800,000 during 2012 and collected $801,000 of cash from customers during the year. Therefore, the company must have had some collections on accounts receivable that were outstanding at the beginning of the year. Let x be the balance in accounts receivable at 12/31/2012. Then:
$100,000 (balance in Gross Accounts Receivable on 12/31/2011) - $1,000 (write-off during 2012) + $800,000 (credit sales during 2012) - x (collections on accounts receivable outstanding at beginning of year) = x + $2,000 (balance in Allowance for Doubtful Accounts at 12/31/2012)
Simplifying the equation, we get:
$899,000 - x = x + $2,000
2x = $897,000
x = $448,500
Therefore, the balance in Gross Accounts Receivable at 12/31/2012 is:
$448,500 + $2,000 (balance in Allowance for Doubtful Accounts at 12/31/2012) = $450,500
So the answer is $450,500 rounded to the nearest thousand, which is $451,000.
Therefore, the company’s balance in Gross Accounts Receivable at 12/31/2012 is $451,000.
Question 1
Suppose that you have purchased a 3-year zero-coupon bond with face value of $1000 and a price of $850. If you hold the bond to maturity, what is your annual return?
*Make sure to input all currency answers without any currency symbols or commas, and use two decimal places of precision.
1 point
Suppose that you have purchased a 3-year zero-coupon bond with face value of $1000 and a price of $850. If you hold the bond to maturity, what is your annual return?
*Make sure to input all currency answers without any currency symbols or commas, and use two decimal places of precision.
1 point
The annual return on a zero-coupon bond is equal to the yield to maturity (YTM). We can use the formula for YTM to solve for the annual return:
PV = FV/(1+r)^n
Where:
PV = present value (price) = $850
FV = future value (face value) = $1000
r = yield to maturity (annual return)
n = number of periods = 3 years
Plugging in the values, we get:
$850 = $1000/(1+r)^3
Multiplying both sides by (1+r)^3, we get:
(1+r)^3 = $1000/$850
Simplifying the right side, we get:
(1+r)^3 = 1.17647
Taking the cube root of both sides, we get:
1+r = 1.045
Subtracting 1 from both sides, we get:
r = 0.045 or 4.5%
Therefore, the annual return, or yield to maturity, on the 3-year zero-coupon bond is 4.5%.
PV = FV/(1+r)^n
Where:
PV = present value (price) = $850
FV = future value (face value) = $1000
r = yield to maturity (annual return)
n = number of periods = 3 years
Plugging in the values, we get:
$850 = $1000/(1+r)^3
Multiplying both sides by (1+r)^3, we get:
(1+r)^3 = $1000/$850
Simplifying the right side, we get:
(1+r)^3 = 1.17647
Taking the cube root of both sides, we get:
1+r = 1.045
Subtracting 1 from both sides, we get:
r = 0.045 or 4.5%
Therefore, the annual return, or yield to maturity, on the 3-year zero-coupon bond is 4.5%.
1 answer