Please help me with this EXPLANTION

[ewoj]

QUESTION:Ralph buys a perpetuity-due paying 500 annually. He deposits the payments into a savings account earning interest at an effective annual rate of 10%. Ten years later, before receiving eleventh payment, Ralph sells the perpetuity based on an effective annual interest rate of 10%. Using the proceeds from the sale plus the money in the savings account, Ralph purchased an annuity due paying X per year for 20 years at an effective annual rate of 10%. Calculate X. [SOA 11/92 #4]
SOLUTION:
The solution is shown below but can someone explain to me how they wrote that equation for the ( MONEY IN THE SAVINGS ACCOUNT portion.. ie 500x1.1 divided by 0.1 part. i dont understand that portion of the equation.

[Gandalf]

500*1.1/.1 = 500/d is the amount he sells the perpetuity-due for. The other piece is the money in the savings account.

[BadBeatMe]

As Gandalf said, 500*1.1/.1 is the amount he sells the perpetuity-due for. Note that this is also what he paid for it, at the time of the sale he is selling a perpetuity-due of 500 annually which is exactly what he bought 10 years earlier.

The money in the savings account part, the left side, is simply the accumulated value of an annuity-due of 500 a year after 10 years. Since the money is coming from a perpetuity-due, the first payment is immediate, 10 payments are accumulated to immediately before the 11th payment, which is exactly what the FV of an annuity-due is.

Remember the formula for the PV of a perpetuity-immediate is 1/i. The reason the formula for the PV of this perpetuity-due is 500*1.1/.1 is the interest is 10% effective, the payment is 500 per year and we need to bring it forward a year because it is due, hence multiplying by 1.1.

[Felicia_lai]

1. at the end of 10 years before the 11th payment recieved,
the saving is : 500 S (due angle n=10 @10%)
2. sell price is: 500/d
3. then the sum of that = X a (due angle n=20 @10%)

[ebeebs]

I'm verry curious why somebody registered in January and waited 3 months to make their first post on a thread from 2007.

[BruteForce]

maybe they like to think before they speak... and I mean really think...

[actuary-r]

Originally Posted by BruteForce

maybe they like to think before they speak... and I mean really think...