Mike buys a perpetuity-immediate with varying annual payments. During the first 5 years, the payment is constant and equal to 10. Beginning in year 6, the payments start to increase. For year 6 and all future years, the payment in that year is K% larger than the payment in the year immediately preceding that year, where K < 9.2. At an annual effective interest rate of 9.2%, the perpetuity has a present value of 167.50. Calculate K.

According to the given data we have:

i = 0.092

167.5 = 10a5] at .092 + v^5{10[(1+k)/1.092].....for infinity}

After the 10a5] at .092 component gone from the problem, we have:

128.804 = 10[(1+k) + v + (1+k).....for infinity}

You can turn this into a geometric progression by pulling out

10 * [(1+k)/1.092]...then your left with 1 + (1+k)/1.092 + (1+k)^2/1.092^2....for infinity.

Since the problem says k < .092.. you know that (1+k)/1.092 is eventually going to converge to 0.

Therefore, you'll have 1/(1-(1+k)/1.092) as your geometric sum.

That geometric sum * (10*v^6*(1+K)) then has to equal your constant, 128.804.

After dividing 128.804 by 10*v^6 you get 21.84.

21.84 = (1+k)*[1/(1-(1+k)/1.092)

Solving for (1+k), you get 1.04 so k = .04 or 4%

the camry sales+accord sale=828,000. to make it so the two numbers are 18 thousand apart and still equal 828,000, you first need to find out what half of 828,000 is. 828,000/2=414,000. for the two numbers to equal 828,000, you have to add the same amount as you subtract from the middle. in this case, the number is 9,000 because it's half of 18,000. to equal 828,000, you have to add 9,000 to 414,000 for the camry and subtract 9,000 from 414,000 for the accord. 414,000+9,000=423,000.

414,000-9,000=405,000.

423,000+405,000=828,000.

423,000-405,000=18,

hope it