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?
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
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
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.
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.
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.
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.
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.
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.
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.
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
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.
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
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%.
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%.
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.
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