A. Joe won a lottery jackpot that will pay him $12,000 each year for the next ten years. If the market interest rates are currently 12%, how much does the lottery have to invest today to pay out this prize to Joe over the next ten years?
B. Mary just deposited $33,000 in an account paying 10% interest. She plans to leave the money in this account for seven years. How much will she have in the account at the end of the seventh year?
C. Mary and Joe would like to save up $10,000 by the end of three years from now to buy new furniture for their home. They currently have $2500 in a savings account set aside for the furniture. They would like to make equal year end deposits to this savings account to pay for the furniture when they purchase it three years from now. Assuming that this account pays 8% interest, how much should the year end payments be?
These questions are so outdated, that they're laughable.
Market interest rates at 12%?? What market is that? The market just went down drastically.
Where is Mary getting 10% interest on an account? My savings account barely pays 1%.
If Mary and Joe want $10,000 in three years, they'd better add at least $2,200 a year for the next three years.
Well I guess I came to the wrong place for help. If you didn't know how to answer it maybe you shouldn't have bothered to reply. Oh, and I think that it was pretty obvious that the problems were outdated.
A. To determine how much the lottery has to invest today, we need to calculate the present value of the future cash flows. The formula for present value is:
PV = CF / (1 + r)^n
Where PV is the present value, CF is the cash flow per year, r is the interest rate, and n is the number of years.
In this case, CF is $12,000, r is 12% (0.12), and n is 10.
Plugging in the values, we get:
PV = $12,000 / (1 + 0.12)^10
Simplifying the equation, we have:
PV = $12,000 / (1.12)^10
Using a calculator or spreadsheet, we can evaluate the expression and find that the present value is approximately $38,149.97. Therefore, the lottery needs to invest approximately $38,149.97 today to pay out the prize to Joe over the next ten years.
B. To calculate the final amount in Mary's account at the end of the seventh year, we can use the future value formula:
FV = PV * (1 + r)^n
Where FV is the future value, PV is the present value, r is the interest rate, and n is the number of years.
In this case, PV is $33,000, r is 10% (0.10), and n is 7.
Plugging in the values, we get:
FV = $33,000 * (1 + 0.10)^7
Simplifying the equation, we have:
FV = $33,000 * (1.10)^7
Using a calculator or spreadsheet, we can evaluate the expression and find that the final amount in Mary's account at the end of the seventh year will be approximately $59,748.62.
C. To calculate the year-end payments that Mary and Joe need to make, we can use the present value formula again, but this time we solve for the cash flow per year (CF):
PV = CF / (1 + r)^n
Rearranging the formula, we have:
CF = PV * (1 + r)^n
Where CF is the cash flow per year, PV is the present value (which is the desired future value - the current savings), r is the interest rate, and n is the number of years.
In this case, PV is $10,000 - $2,500 = $7,500, r is 8% (0.08), and n is 3.
Plugging in the values, we get:
CF = $7,500 * (1 + 0.08)^3
Simplifying the equation, we have:
CF = $7,500 * (1.08)^3
Using a calculator or spreadsheet, we can evaluate the expression and find that the year-end payments should be approximately $9,398.54. Therefore, Mary and Joe need to make year-end payments of approximately $9,398.54 to save up $10,000 by the end of three years.