9. (Related to Checkpoint 6.2) (Prosent value of annuity payments) The state lot
ID: 2794842 • Letter: 9
Question
9. (Related to Checkpoint 6.2) (Prosent value of annuity payments) The state lottory's million-dollar payout provides for $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 $75,000 payments occur at the end of each of the next 19 years. 7 percent is the discount rate, whai is the present value of this stream of cash flows? If 14 percent is the discount rate, what is the present value of the cash flows? a. If 7 percent is the discount rate, the present value of the annuity due is $ Round to the nearest cent.) b. If 14 percent is the discount rate, the present value of the annuity due is $ (Round to the nearest cent.) 10. (Related to Checkpoint 6.1) (Annuity payments) Lisa Simpson wants to have $1,700,000 in 55 years by making equal annual end-of-the-year deposits into a tax-deferred account paying 10.50 percent annually. What must Lisa's annual deposit be? The amount of Lisa's annual deposit must be S Round to the nearest cent.) 11. (Related to Checkpoint 6.5) (Present value of a growing perpetuity) What is the present value of a perpetual stream of cash flows that pays $3,500 at the end of year one and the annual cash flows grow at a rate of 2% per year indefinitely. if the appropriate discount rate is 9%? What if the appropriate discount rate is 7%? a. If the appropriate discount rate is 9%, the present value of the growing perpetuity is $ nearest cent) (Round to the b. If the appropriate discount rate is 7%the present value of the growing perpetuity is $ nearest cent.) Round to theExplanation / Answer
Answer 9.
If interest rate is 7%:
Annual Payment = $75,000
Number of Payments = 20
Present Value of Annuity due = $75,000 + $75,000/1.07 + $75,000/1.07^2 + … + $75,000/1.07^19
Present Value of Annuity due = $75,000 * 1.07 * (1 - (1/1.07)^20) / 0.07
Present Value of Annuity due = $75,000 * 11.3356
Present Value of Annuity due = $850,170.00
If interest rate is 14%:
Annual Payment = $75,000
Number of Payments = 20
Present Value of Annuity due = $75,000 + $75,000/1.14 + $75,000/1.14^2 + … + $75,000/1.14^19
Present Value of Annuity due = $75,000 * 1.14 * (1 - (1/1.14)^20) / 0.14
Present Value of Annuity due = $75,000 * 7.55037
Present Value of Annuity due = $566,277.75
Answer 10.
Desired sum in 55 years = $1,700,000
Annual Interest Rate = 10.50%
Future Value of Deposits = $1,700,000
Annual Deposits * (1.1050^55 - 1) / 0.1050 = $1,700,000
Annual Deposits *2,301.1359 = $1,700,000
Annual Deposits = $738.77
Answer 11.
If discount rate is 9%
Year-end Payment = $3,500
growth rate = 2%
PV of Perpetuity = Year-end Payment / (discount rate - growth rate)
PV of Perpetuity = $3,500 / (0.09 - 0.02)
PV of Perpetuity = $50,000.00
If discount rate is 7%
Year-end Payment = $3,500
growth rate = 2%
PV of Perpetuity = Year-end Payment / (discount rate - growth rate)
PV of Perpetuity = $3,500 / (0.07 - 0.02)
PV of Perpetuity = $70,000.00
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