Hi, would anyone be willing to help with this. Thanks :)
2. Find the following values:
a) An intial $500 compounded for 10 years at 6 percent
b) An intial $500 compounded for 10 years at 12 percent
c) The present value of $500 due in 10 years at a 6 % discount rate.
d) The present value of $1, 552.90 due in 10 years at a 12 % discount rate and at a 6% rate. Give a verbal definition of the term present value, and illustrate it using a time line with data from this problem. As a part of your answer, explain why present values are dependent upon interest rates.
3. To the closest year, how long will it take $200 to double if it is deposited and earns the following rates?
a) 7%
b) 10%
c) 18%
d) 100%
4. Find the future value of the following annuities. The first payment in these annuities is made at the end of Year 1; that is, they are ordinary annuities.
a) $400 per year for 10 years at 10%
b) $200 per year for 5 years at 5 %
c) $400 per year for 5 years at 0 %
d) Now rework parts a, b, c assuming that payments are made at the beginning of each year; that is, they are annuities due.
5. Find the present value of the following ordinary annuities:
a) $400 per year for 10 years at 10%
b) $200 per year for 5 years at 5%
c) $400 per year for 5 years at 0%
d) Now rework parts a, b, and c assuming that payments are made at the beginning of each year; that is, they are annuities due.
14. Washington-Pacific invests $4 million to clear a tract of land and to set out some young pine trees. The trees will mature in 10 years, at which time Washington-Pacific plans to sell the forest at an expected price of $8 million. What is Washington-Pacific’s expected rate of return?
18. You need to accumulate $10,000. To do so, you plan to make deposits of $1,250 per year, with the first payment being made a year from today, in a bank accountant that pays 12% annual interest. Your last deposit will be less than $1,250 if less is needed to round out to $10,000. How many years will it take you to reach your $10,000 goal, and how large will the last deposit be?
Sure, I can help with that! Let's break it down step by step:
Problem 2:
a) To find the future value of an initial $500 compounded for 10 years at 6 percent, we can use the formula for compound interest: FV = PV * (1 + r)^n. Plugging in the values, FV = 500 * (1 + 0.06)^10. Calculate the value to find the future value after 10 years.
b) Similarly, to find the future value of an initial $500 compounded for 10 years at 12 percent, use the formula: FV = 500 * (1 + 0.12)^10. Calculate the value to find the future value after 10 years.
c) To find the present value of $500 due in 10 years at a 6% discount rate, we can use the formula for present value: PV = FV / (1 + r)^n. Plugging in the values, PV = 500 / (1 + 0.06)^10. Calculate the value to find the present value.
d) The present value is the current value of a future cashflow. In this case, it represents the value of $1,552.90 due in 10 years. The present value depends on the discount rate used. A higher discount rate would result in a lower present value. To find the present value of $1,552.90 due in 10 years at a 12% discount rate and at a 6% rate, use the present value formula for each rate. Calculate the values to find the present value of the cashflow at each rate.
To find the answers to these financial questions, we can utilize various formulas and concepts. Let's go through each question one by one and explain the steps to find the answers.
2a) To find the future value of an initial amount of $500 compounded for 10 years at a 6% interest rate, we can use the compound interest formula:
Future Value = Present Value * (1 + Interest Rate)^Time
In this case, the Present Value is $500, the Interest Rate is 6% (or 0.06 in decimal form), and the Time is 10 years. Plugging these values into the formula, we get:
Future Value = $500 * (1 + 0.06)^10
By calculating this expression, we can find the future value.
2b) Similarly, to find the future value of an initial amount of $500 compounded for 10 years at a 12% interest rate, we use the same formula but with the new interest rate:
Future Value = $500 * (1 + 0.12)^10
2c) The present value is the amount of money today that is equivalent to a future cash flow or investment at a certain discount rate. To find the present value of $500 due in 10 years at a 6% discount rate, we can use the present value formula:
Present Value = Future Value / (1 + Discount Rate)^Time
In this case, the Future Value is $500, the Discount Rate is 6% (or 0.06 in decimal form), and the Time is 10 years. Plugging these values into the formula, we get:
Present Value = $500 / (1 + 0.06)^10
2d) Present value is the concept of determining the value of future cash flows today, taking into account a discount rate that represents the opportunity cost of investing in different assets. The present value formula considers the discounted cash flows:
Present Value = Future Value / (1 + Discount Rate)^Time
In this case, we have two different discount rates: 12% and 6%. To find the present value of $1,552.90 due in 10 years at a 12% discount rate, we use the formula with the appropriate values:
Present Value (12%) = $1,552.90 / (1 + 0.12)^10
Similarly, to find the present value at a 6% discount rate, we use the formula:
Present Value (6%) = $1,552.90 / (1 + 0.06)^10
By calculating these expressions, we can find the present values at different discount rates.
3a) To find the number of years it takes for $200 to double at a 7% interest rate, we can use the compound interest formula and solve for time:
Future Value = Present Value * (1 + Interest Rate)^Time
In this case, the Present Value is $200, the Interest Rate is 7% (or 0.07 in decimal form), and the Future Value is 2 times the Present Value ($400). We need to solve for Time:
$400 = $200 * (1 + 0.07)^Time
By rearranging the equation and using logarithms or trial-and-error, we can find the time it takes for $200 to double.
Repeat the above steps for parts (b), (c), and (d) with the given interest rates to find the respective time durations for doubling the money.
4a) To find the future value of an ordinary annuity that pays $400 per year for 10 years at a 10% interest rate, we can use the formula for the future value of an ordinary annuity:
Future Value = Payment * [(1 + Interest Rate)^Time - 1] / Interest Rate
In this case, the Payment per year is $400, the Interest Rate is 10% (or 0.10 in decimal form), and the Time is 10 years. Plugging these values into the formula, we get:
Future Value = $400 * [(1 + 0.10)^10 - 1] / 0.10
By calculating this expression, we can find the future value of the annuity.
Repeat the above steps for parts (b) and (c) with the given annuity details and interest rates to find the respective future values of the annuities.
To rework parts (a), (b), and (c) assuming payments are made at the beginning of each year (annuities due), we need to adjust the formula slightly. Multiply the payment by (1 + the interest rate) before using the formula to calculate the future value.
5a) To find the present value of an ordinary annuity that pays $400 per year for 10 years at a 10% interest rate, we can use the formula for the present value of an ordinary annuity:
Present Value = Payment * [1 - (1 + Interest Rate)^(-Time)] / Interest Rate
In this case, the Payment per year is $400, the Interest Rate is 10% (or 0.10 in decimal form), and the Time is 10 years. Plugging these values into the formula, we get:
Present Value = $400 * [1 - (1 + 0.10)^(-10)] / 0.10
By calculating this expression, we can find the present value of the annuity.
Repeat the above steps for parts (b) and (c) with the given annuity details and interest rates to find the respective present values of the annuities.
To rework parts (a), (b), and (c) assuming payments are made at the beginning of each year (annuities due), we need to adjust the formula slightly. Divide the payment by (1 + the interest rate) before using the formula to calculate the present value.
14) To find Washington-Pacific's expected rate of return, we use the formula for the rate of return:
Rate of Return = (Future Value - Initial Investment) / Initial Investment
In this case, the Initial Investment is $4 million and the Future Value is expected to be $8 million. Plugging these values into the formula, we get:
Rate of Return = ($8 million - $4 million) / $4 million
By calculating this expression, we can find the expected rate of return.
18) To accumulate $10,000 by making annual deposits of $1,250 at a 12% annual interest rate, we need to find the number of years it will take to reach the goal and the amount of the last deposit. We can use the formula for the future value of an ordinary annuity to solve for time:
Future Value = Payment * [(1 + Interest Rate)^Time - 1] / Interest Rate
In this case, the Payment per year is $1,250, the Interest Rate is 12% (or 0.12 in decimal form), and the Future Value is $10,000. We need to solve for Time:
$10,000 = $1,250 * [(1 + 0.12)^Time - 1] / 0.12
By rearranging the equation and using logarithms or trial-and-error, we can find the time it takes to reach the goal and the value of the last deposit.
I hope this explanation helps you in solving the given financial questions. If you have further doubts or need more assistance, feel free to ask.
14. The rate of return depends partly upon what they netted from the sale of lumber. A doubling of land value in 10 years amounts to a average annual 7.2% capital gain, but presumably there was additional income from logging activity.
We do not take tests or do homework for people here. If you would present one or two questions per post and show your own work or thoughts, someome will be glad to assist you.