has an investment worth $56,000. The investment will make a special, extra payment of X to XYZ in 2 years from today. The invest
ment also will make regular, fixed annual payments of $12,000 to XYZ with the first of these payments made to XYZ in 1 year from today and the last of these annual payments made to XYZ in 5 years from today. The expected return for the investment is 13.2 percent per year. What is X, the amount of the special payment that will be made to XYZ in 2 years
1 answer:
Answer:
The payment X that will be made two years from now is approx $17940.
Explanation:
The present value of the investment is $56000. To calculate the value of X, we first need to calculate the present value of the fixed annual payments made to XYZ.
The fixed annual payments made to XYZ is an annuity as the payments is fixed, is paid out after equal intervals of time and for a limited time period.
To calculate the present value of annuity, we will use the attached formula.
PV of annuity = 12000 * [(1 - (1+0.132)^-5) / 0.132]
PV of annuity = $42001.62278 rounded off to $42001.62 or we can round it off to be approx $42000
If the present value of fixed payments is $42000, the present value of X should be,
Present value of X = 56000 - 42000 = $14000
To calculate the value of X that will be paid in 2 years, we will calculate the future value of $14000 after 2 years. The formula for future value is as follows,
FV = PV * (1+r)^t
Where,
- r is the rate of return
- t is the time periods
FV of X= 14000 * (1+0.132)^2
FV of X = $17939.936 rounded off to approx $17940
So, the payment X that will be made two years from now is approx $17940.
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