Question

Sam buys a perpetuity paying $5,000 every three years, starting immediately. He deposits the payments into a savings account earning interest at an effective interest rate of 5%. Twelve years later, before receiving the fifth payment, Sam sells the perpetuity based on an effective annual interest rate of 5%. Using proceeds from the sale plus the money in the savings account, he purchases an annuity paying P at the end of every two years for twenty years at an annual effective interest rate of 5%.

His savings account balance immediate before the 5th payment. Find the balance to the nearest cent.

Sam sells the perpetuity for 36,721 rounded to the nearest dollar. Find the sale price to the nearest cent.

Find P. Answer to the nearest cent.

Answer 1

1.

Year	Receipt	No of years ahead	Compound factor @ 5%	Balance
0	$     5,000	12	1.795856	$ 8,979.28
3	$     5,000	9	1.551328	$ 7,756.64
6	$     5,000	6	1.340096	$ 6,700.48
9	$     5,000	3	1.157625	$ 5,788.13
			Savings	$29,224.53

2.

Formula for Perpetuity price(Due): (Receipt/Discount rate) * 1.05

In the given case the receipt is $5000 but is received every three years. The amount can be converted into an infinite value by dividing its present value using the AF factor for one life cycle (3 years) and Dividing the result by 5%.

Sale proceeds of Perpetuity (Due) = R/D * 1.05 = [5000/AF (5%, 3yrs)]/5% * 1.05 = $30,845.50

3. P = Savings + Sale proceeds of perpetuity = $29,224.53 + $30,845.50

                                                                               = $60,070

Please, Please Upvote if you like the answer.