Hello! I am not very sure if i title this correctly or if it under the correct topic but i really need help with this question.
The present value (PV) of a stream of income is \(\displaystyle D_t,\, t\, =\, 0,\, 1,\, ...,\, T\) is defined as
. . . . .\(\displaystyle \displaystyle PV\, =\, \sum_{i=0}^T\, \dfrac{D_t}{(1\, +\, r)^t}\)
where \(\displaystyle t\, =\ 0\) is the current year and \(\displaystyle r\) is the rate of interest.
i. Compute the present value of a winning lottery ticket that will pay $200,000 per year for 20 years starting in the present year. Assume an interest rate of 12%. Solve the same problem assuming interest rates of 15% and 20%. [Hint: For instance rate of 12%, \(\displaystyle r\, =\, 0.12.\)]
ii. Compute the value of a government bond that pays one dollar every year in perpetuity (i.e., forever) given the interest rate of \(\displaystyle r.\)
[Removed imgur links, my bad]
The answer for 12% is apparently 1,673,155.37
From what I understand about the question is that, every year, the $200 000 drops to a lower value because of the interest rate (12%).
What i have tried was to find the first and last element using the equation given.
Then i tried to put it into the equation needed to find the sum of the geometric series (i also tried arithmetic)
Thank you!!
The present value (PV) of a stream of income is \(\displaystyle D_t,\, t\, =\, 0,\, 1,\, ...,\, T\) is defined as
. . . . .\(\displaystyle \displaystyle PV\, =\, \sum_{i=0}^T\, \dfrac{D_t}{(1\, +\, r)^t}\)
where \(\displaystyle t\, =\ 0\) is the current year and \(\displaystyle r\) is the rate of interest.
i. Compute the present value of a winning lottery ticket that will pay $200,000 per year for 20 years starting in the present year. Assume an interest rate of 12%. Solve the same problem assuming interest rates of 15% and 20%. [Hint: For instance rate of 12%, \(\displaystyle r\, =\, 0.12.\)]
ii. Compute the value of a government bond that pays one dollar every year in perpetuity (i.e., forever) given the interest rate of \(\displaystyle r.\)
[Removed imgur links, my bad]
The answer for 12% is apparently 1,673,155.37
From what I understand about the question is that, every year, the $200 000 drops to a lower value because of the interest rate (12%).
What i have tried was to find the first and last element using the equation given.
Then i tried to put it into the equation needed to find the sum of the geometric series (i also tried arithmetic)
Thank you!!
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