Visualize a scenario related to financial growth and stability. Create an art piece themed around investment, showcasing a money tree gleaming with golden coins, symbolizing an investment that keeps giving returns over a period of time. The tree is planted in a pot that has the number '6%' etched into it, representing the annual interest rate. Rays of light, emanating from the pot, symbolize the bright prospects of an investment. The setting is warm, the sunlight shines off of the leaves and the coins, and the entire scene has an aurora of prosperity, yet there is no text in the image.

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.