After a protracted legal case, Joe won a settlement that will pay him $11,000 each year at the end of the year for the next ten years. If the market interest rates are currently 5%, exactly how much should the court invest today, assuming end of year payments, so there will be nothing left in the account after the final payment is made?
Mary just deposited $33,000 in an account paying 7% interest. She plans to leave the money in this account for eight 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 $1500 in a savings account set aside for the furniture. They would like to make three 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 6% interest, how much should the year end payments be?
To find the amount that the court should invest today in order to have nothing left in the account after the final payment is made, we can use the present value formula.
The present value formula is given by: PV = PMT / (1 + r)^n, where PV is the present value, PMT is the annual payment, r is the interest rate, and n is the number of years.
In this case, the annual payment (PMT) is $11,000, the interest rate (r) is 5%, and the number of years (n) is 10.
Plugging these values into the formula, we have: PV = $11,000 / (1 + 0.05)^10.
Calculating this expression, we get: PV = $11,000 / 1.62889.
Therefore, the court should invest approximately $6,767.82 today in order to have nothing left in the account after the final payment is made.
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To find out 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 formula is given by: 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, the present value (PV) is $33,000, the interest rate (r) is 7%, and the number of years (n) is 7.
Plugging these values into the formula, we have: FV = $33,000 * (1 + 0.07)^7.
Calculating this expression, we get: FV = $33,000 * 1.512981.
Therefore, Mary will have approximately $49,795.76 in her account at the end of the seventh year.
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To find out how much the year-end payments should be in order to save up $10,000 in three years, we can use the future value formula again.
In this case, the present value (PV) is $1500, the future value (FV) is $10,000, the interest rate (r) is 6%, and the number of years (n) is 3.
Plugging these values into the formula, we have: FV = PV * (1 + r)^n.
Rearranging the formula to solve for PV, we get: PV = FV / (1 + r)^n.
Substituting the given values, we have: PV = $10,000 / (1 + 0.06)^3.
Calculating this expression, we get: PV = $10,000 / 1.191016.
Therefore, the year-end payments should be approximately $8,387.90 in order to save up $10,000 in three years.