HI, could anyone help with this please. :)
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?
1. we34
Sure, I can help you with these questions! Let's go through each question and explain how to find the answers.
2. a) To find the future value of an initial $500 compounded for 10 years at 6 percent, you can use the formula for compound interest: Future Value = Principal * (1 + Interest Rate)^Time. Plugging in the values, you get Future Value = $500 * (1 + 0.06)^10.
b) Similarly, for an initial $500 compounded for 10 years at 12 percent, you use the same formula, but with a different interest rate: Future Value = $500 * (1 + 0.12)^10.
c) To find the present value of $500 due in 10 years at a 6% discount rate, you can use the formula for present value: Present Value = Future Value / (1 + Interest Rate)^Time. Plugging in the values, you get Present Value = $500 / (1 + 0.06)^10.
d) To find the present value of $1,552.90 due in 10 years at a 12% discount rate and at a 6% rate, you use the same formula, but with different interest rates: Present Value = $1,552.90 / (1 + 0.12)^10 and Present Value = $1,552.90 / (1 + 0.06)^10.
Present value is the current worth of a future sum of money, discounted back to the present using an appropriate interest rate. It represents the value of the future cash flows in today's dollars. A time line with data from this problem would show the future cash flows (the initial investment and the future value) at their respective time points, and the present value is the sum of the discounted future cash flows. Present values are dependent upon interest rates because the interest rate determines the discount rate applied to future cash flows. A higher interest rate means a higher discount rate, which reduces the present value of future cash flows.
3. To find how long it will take $200 to double at different interest rates, you can use the formula for compound interest: Time = log(2) / log(1 + Interest Rate/100). Plugging in the values, you get Time = log(2) / log(1 + 0.07) for 7%, Time = log(2) / log(1 + 0.1) for 10%, Time = log(2) / log(1 + 0.18) for 18%, and Time = log(2) / log(1 + 1) for 100%.
4. To find the future value of ordinary annuities (payment made at the end of each year), you can use the formula for future value of an annuity: Future Value = Payment * [(1 + Interest Rate)^Time - 1] / Interest Rate. Plug in the values for each annuity to get the future value.
5. To find the present value of ordinary annuities (payment made at the end of each year), you can use the formula for present value of an annuity: Present Value = Payment * [1 - (1 + Interest Rate)^(-Time)] / Interest Rate. Plug in the values for each annuity to get the present value.
14. To find the expected rate of return for Washington-Pacific's investment, you need to calculate the rate of return on the investment. The rate of return can be found using the formula: Rate of Return = (Ending Value - Beginning Value) / Beginning Value * 100%. Plug in the values to get the expected rate of return.
18. To determine how many years it will take to reach the $10,000 goal, you can use the formula for future value of an annuity: Time = log(Target Value / Payment) / log(1 + Interest Rate). Plug in the values to get the time. The last deposit can be calculated by subtracting the sum of the previous deposits from the target value.
I hope this helps! Let me know if there's anything else I can assist you with.