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Sasha has an investment worth 40,434 dollars. The investment will make a special payment of X...

Sasha has an investment worth 40,434 dollars. The investment will make a special payment of X to Sasha in 6 years from today. The investment also will make regular, fixed annual payments of 6,000 dollars to Sasha with the first of these payments made to Sasha later today and the last of these annual payments made to Sasha in 10 years from today. The expected return for the investment is 13.1 percent per year. What is X, the amount of the special payment that will be made to Sasha in 6 years?

Expert Solution

Sasha has an investment worth 40,434 dollars. The investment will make a special payment of X to Sasha in 6 years from today. The investment also will make regular, fixed annual payments of 6,000 dollars to Sasha with the first of these payments made to Sasha later today and the last of these annual payments made to Sasha in 10 years from today. The expected return for the investment is 13.1 percent per year. What is X, the amount of the special payment that will be made to Sasha in 6 years?

Investment worth available today to Sasha(Present Value) = $40,434

Investment will make Special payment in 6 years and regular fixed monthly payment forever to Sasha

Calculating the Present Value of regular fixed monthly payment with 1st payment been made today and last payment maded 10 years from today to Sasha:-

Where, C= Periodic Payments = $6000

r = Periodic Interest rate = 13.1%

n= no of periods = 10

Present Value = $38,427.76

Now, the Special Payment in 6 years has a Present value today of = Investment worth Today - Present value of Regular Payments

=$40,434 - $38,427.76

= $2006.24

Now Calculating the value of Special Payment in 6 years:-

where, Future Value= X

r = periodic interest rate = 13.1% (per month)

n = no of periods = 6 years

Present Value = $2006.24

Future value = $4199.12

So, Value of X, the amount of the special payment that will be made to Sasha in 6 year(s) is $4199.12

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jeff jeffy answered 2 years ago

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