Answer:
(a) $4,040
(b) $3,434
(c) $348
(d) $3,265
Explanation:
(a) Calculate the following: The future value of lump-sum investment of $3,200 in four years that earns 6 percent. Round your answer to the nearest dollar. (Hint: Use Appendix A.1 or the Garman/Forgue companion website.) Round Future value of a Single Amount in intermediate calculations to four decimal places. $
To estimate this, the formula for calculating future value is used as follows:
FV = PV * (1 + r)^n ………………………….. (1)
Where,
FV = future value = ?
PV = lump-sum investment = $3,200
r = interest rate = 6%, or 0.06
n = number of years = 4
Substitute the values into equation (1) to have:
FV = $3,200 * (1 + 0.06)^4
FV = $3,200 * (1.06)^4
FV = $3,200 * 1.2625
FV = $4,040
(b) The future value of $1,100 saved each year for three years that earns 4 percent. Round your answer to the nearest dollar. (Hint: Use Appendix A.3 or the Garman/Forgue companion website.) Round Future value of Series of Equal Amounts in intermediate calculations to four decimal places. $
To calculate this, the formula for calculating the Future Value (FV) of an Ordinary Annuity is used as follows:
FV = M * (((1 + r)^n - 1) / r) ................................. (2)
Where,
FV = Future value of the amount after 3 years =?
M = Annual savings = $1,100
r = interest rate = 4%, or 0.04
n = number of years = 3
Substituting the values into equation (2), we have:
FV = $1,100 * (((1 + 0.04)^3 - 1) / 0.04)
FV = $1,100 * 3.1216
FV = $3,434
(c) A person who invests $1,800 each year finds one choice that is expected to pay 4 percent per year and another choice that may pay 7 percent. What is the difference in return if the investment is made for four years? Round your answer to the nearest dollar. (Hint: Use Appendix A.3 or the Garman/Forgue companion website.) Round Future value of Series of Equal Amounts in intermediate calculations to four decimal places. $
To do this, we first calculate the return of each of the 2 investments by using the the formula for calculating the Future Value (FV) of an Ordinary Annuity in part b above is used as follows:
<u>Calculation of return at 4 percent</u>
Where;
FV at 4% = Future value of the return after 4 years =?
M = Annual savings = $1,800
r = interest rate = 4%, or 0.04
n = number of years = 4
Substituting the values into equation (2), we have:
FV at 4% = $1,800 * (((1 + 0.04)^4 - 1) / 0.04)
FV at 4% = $1,800 * 4.2465
FV at 4% = $7,644
<u>Calculation of return at 7 percent</u>
Where;
FV at 7% = Future value of the return after 4 years =?
M = Annual savings = $1,800
r = interest rate = 7%, or 0.07
n = number of years = 4
Substituting the values into equation (2), we have:
FV at 7%= $1,800 * (((1 + 0.07)^4 - 1) / 0.07)
FV at 7% = $1,800 * 4.4399
FV at 7% = $7,992
<u>Calculation of the difference in return</u>
This is calculated as follows:
Difference = FV at 7% - FV at 4% = $7,992 - $7,644 = $348
(d) The amount a person would need to deposit today with a 7 percent interest rate to have $4,000 in three years. Round your answer to the nearest dollar. (Hint: Use Appendix A.2 or the Garman/Forgue companion website.) Round Present value of a Single Amount in intermediate calculations to four decimal places. $
To estimate this, the formula for calculating present value is used as follows:
PV = FV / (1 + r)^n ………………………….. (1)
Where;
PV = Present value or amount to deposit today = ?
FV = future value in three years = $4,000
r = interest rate = 7%, or 0.07
n = number of years = 3
Substitute the values into equation (1) to have:
PV = $4,000 / (1 + 0.07)^3
PV = $4,000 / 1.2250
PV = $3,265