9 (Related to Checkpoint 6.2) (Present value of annuity payments) The state lott
ID: 2794961 • Letter: 9
Question
9 (Related to Checkpoint 6.2) (Present value of annuity payments) The state lottery's million-dollar payout $1.5 million to be paid in 20 installments of $75,000 per payment The first $75,000 payment is made immediately, and the 19 remaining $75,00 present value of this stream of cash fows? if14 percent is the discount rate, what is the present a. If 7 percent is the discount rate, the present value of the annuity due is $ 0 payments occur at the end of each of the next 19 years it 7 percent is the discount rate, what is the Round to the nearest cent If 14 percent is tho discount rate, the present value of the annuity due is $ Round to the nearest cent b. …Explanation / Answer
a. The present value of such series of cash flows can be calculated with formula of the present value (PV) of annuity due. Annuity due is like ordinary annuity but the amount is due at the starting of the period.
Formula of the present value (PV) of annuity due
PV = C * [1- (1+i) ^-n / i] * (1+i)
Where,
Present value PV =?
C is annuity cash flow = $75,000 per annum
Discount rate i = 7% per annum
Time period of annuity n = 20 years
Therefore,
PV = $75,000 * [1- (1+7%) ^-20 / 7%] * (1+7%)
PV = $850,169.64
b. If Discount rate i = 14% per annum
Then present value,
PV = $75,000 * [1- (1+14%) ^-20 / 14%] * (1+14%)
PV = $566,277.66
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