d. Assume that a college parking sticker today costs $90. If the cost of parking
ID: 2436454 • Letter: D
Question
d.Assume that a college parking sticker today costs $90. If the cost of parking is increasing at the rate of 5% per year, how much will the college parking sticker cost in eight years?(Round your answer to 2 decimal places.)
e.Assume that the average price of a new home is $158,500. If new homes are increasing at a rate of 10% per year, how much will a new home cost in eight years?(Round your answer to 2 decimal places.)
f.An investment will pay you $10,000 in 10 years, and it will also pay you $400 at the end of each of the next 10 years (years 1 thru 10). If the annual interest rate is 6%, how much would you be willing to pay today for this type of investment? (Round your answer to nearest whole dollar.)
g.A college student is reported in the newspaper as having won $10,000,000 in the Kansas State Lottery. However, as is often the custom with lotteries, she does not actually receive the entire $10 million now. Instead she will receive $500,000 at the end of the year for each of the next 20 years. If the annual interest rate is 6%, what is the present value (today’s amount) that she won? (Ignore taxes.)
Explanation / Answer
1.
Formula for compound interest can be used to compute increase in price as:
A = P x (1 + r/n) nxt
A = Future cost of parking sticker
P = Principal = Present value of price = $ 90
r = Rate of interest = 5 % or 0.05 p.a.
n = No. of compounding in a year = 1
t = No. of years = 8
Cost of sticker in eight years = $ 90 x (1 +0.05)8
= $ 90 x (1.05)8
= $ 90 x 1.477
= $ 132.97
2.
Formula for compound interest can be used to compute increase in price of home as:
A = P x (1 + r/n) nxt
A = Future value of home
P = Principal = Present value of home = $ 158,500
r = Rate of interest = 10 % or 0.1 p.a.
n = No. of compounding in a year = 1
t = No. of years = 8
Cost of home in eight years = $ 158,500 x (1 + 0.1)8
= $ 158,500 x (1.1)8
= $ 158,500 x 2.144
= $ 339,758.83
3.
PV of a single amount= Future amount x PVIF (i, n)
PV of ordinary annuity = Future cash flow x PVIFA (i, n)
Where i = interest rate and n = no. of years
Present value of investment = PV of $ 10,000 + PV of $ 400 as annuity
= $ 10,000 x PVIF (6 %, 10) + $ 400 x PVIFA (6 %, 10)
= ($ 10,000 x 0.5584) + ($ 400 x 7.3601)
= $ 5,584 + $ 2,944.04 = $ 8,528.04
Today $ 8,528.04 should be paid for the investment.
4.
PV of ordinary annuity = C x PVIFA (i, n)
Where
C = Periodic cash flow = $ 500,000
i = interest rate = 6 % or 0.06 p.a.
n = no. of periods = 20
PV = $ 500,000 x PVIFA (6 %, 20)
= $ 500,000 x 11.470
= $ 5,735,000
Present value of winnings is $ 5,735,000.
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