question archive 1) What is the present value of a series of payments received each year for 5 years, starting with $200 paid one year from now and the payment growing in each subsequent year by 1%? Assume a discount rate of 2%
1) What is the present value of a series of payments received each year for 5 years, starting with $200 paid one year from now and the payment growing in each subsequent year by 1%? Assume a discount rate of 2%
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1) What is the present value of a series of payments received each year for 5 years, starting with $200 paid one year from now and the payment growing in each subsequent year by 1%? Assume a discount rate of 2%.
Please round your answer to the nearest hundredth.
2) What is the present value of a series of payments received each year for 9 years, starting with $300 paid one year from now and the payment growing in each subsequent year by 3%? Assume a discount rate of 5%.
Please round your answer to the nearest hundredth.
3) What is the present value of a series of payments received each year forever, starting with $100 paid one year from now and the payment growing in each subsequent year by 6%? Assume a discount rate of 9%.
Please round your answer to the nearest hundredth.
4) What is the present value of a series of payments received each year forever, starting with $300 paid one year from now and the payment growing in each subsequent year by 10%? Assume a discount rate of 12%.
Please round your answer to the nearest hundredth.
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Answer:
Present value of growing annuity
= P*[1 - [(1+g) / (1+r)]^n] / (r-g)
Where P = annual payments
r = rate of interest
g = growth rate
1)
= 200*[1 - [(1+1%) / (1+2%)]^5] / (2% - 1%)
= 961.36 i.e., 1000(rounded to nearest 100th)
2)
= 300*[1 - [(1+3%)/(1+5%)]^9] / (5% - 3%)
= $2400(rounded to nearest 100th)
3)
Present value of growing perpetuity = cashflow / (r - g)
r = discount rate
g = growth rate
= 100 / (9% - 6%)
= $3,300
4)
Using the same formula as above
= 300 / (12% - 10%)
= 300 / 2%
= $15,000
