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?
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?
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?
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Brent A. Spooner
FIN110-0703A-04
Unit 1 Individual Project
July 16, 2007
Personal Finance Concepts
A.
To calculate how much the lottery needs to invest today to pay out the prize over the next ten years, we can use the present value formula. The present value is the current value of future cash flows, taking into account the time value of money.
The formula for present value is:
PV = CF / (1 + r)^n
Where PV is the present value, CF is the cash flow, r is the interest rate, and n is the number of periods.
In this case, the cash flow is $12,000 per year for ten years, the interest rate is 12%, and the number of periods is ten. Plugging these values into the formula, we get:
PV = $12,000 / (1 + 0.12)^10
Calculating the present value using a calculator or spreadsheet, the lottery needs to invest approximately $63,105.30 today to pay out the prize.
To calculate how much Mary will have in her account at the end of the seventh year, we can use the future value formula. The future value is the value of an investment at a specific time in the future, taking into account the interest earned.
The formula for future value is:
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 periods.
In this case, the present value is $33,000, the interest rate is 10%, and the number of periods is seven. Plugging these values into the formula, we get:
FV = $33,000 * (1 + 0.10)^7
Calculating the future value using a calculator or spreadsheet, Mary will have approximately $58,785.02 in her account at the end of the seventh year.
To calculate how much the year-end payments should be to save up $10,000 in three years, we can use the future value of an ordinary annuity formula. An ordinary annuity is a series of equal cash flows received or paid at the end of each period.
The formula for the future value of an ordinary annuity is:
FV = PMT * [(1 + r)^n - 1] / r
Where FV is the future value, PMT is the payment amount, r is the interest rate, and n is the number of periods.
In this case, the future value is $10,000, the interest rate is 8%, and the number of periods is three. We need to solve for PMT. Plugging these values into the formula and rearranging to solve for PMT, we get:
PMT = FV * r / [(1 + r)^n - 1]
PMT = $10,000 * 0.08 / [(1 + 0.08)^3 - 1]
Calculating the year-end payment using a calculator or spreadsheet, the payments should be approximately $3,181.67 each year to reach the savings goal of $10,000 in three years.