Question

1. You just inherited some money, and a broker offers to sell you an annuity that pays $32,200 at the end of each year for 50 years. You could earn 8% on your money in other investments with equal risk. What is the most you should pay today for the annuity?  

2. You have a chance to buy an annuity that pays $85,000 at the beginning of each year for 20 years. You could earn 12.5% on your money in other investments with equal risk. What is the most you should pay for the annuity?

3. Your father LeBron paid $230,000 for an investment that promises to pay $4,500 at the end of each of the next 5 years, then an additional lump sum payment of $25,500 at the end of the 6^thyear. What is the expected rate of return (IRR) on this investment?

Answer 1

Ans 1) $ 391471.51

Annuity PV Factor (End of Year) =	P [ 1 - ( 1 + r )-n ]
	r
	32000* ( 1 - ((1 / (1 + 8%)^50)))
	8%
	31317.72069
	0.08
	391471.51

Answer 2

SOLUTION :

1.

Amount that can be paid should be at most equal to the PV of the annuity.

Annuity details :

Annuity amount, A = $32200 at the end of each year.

Period of annuity, n = 50 years

Return rate , r = 8% = 0.08

=> (1+r) = 1.08

PV of annuity 

= A (1 + r) ((1 +r)^n - 1) / (r(1+r)^n)

= 32200 (1.08^50 - 1) / (0.08*1.08^50)

= 393918.21 ($) 

So, amount that can be paid for the proposed annuity 

= at most $393,918.21  (ANSWER).

2.

Amount that can be paid should be at most equal to the PV of the annuity.

Annuity details :

Annuity amount, A = $85000 at the beginning of each year.

Period of annuity, n = 20 years

Return rate , r = 12.5% = 0.125

=> (1+r) = 1.125 

It is annuity due as payments are made in the beginning of each year.

PV of annuity 

= A (1 + r) ((1 +r)^n - 1) / (r(1+r)^n)

= 85000*1.125 (1.125^20 - 1) / (0.125*1.125^20)

= 692454.42 ($) 

So, amount that can be paid for the proposed annuity 

= at most $692,454.42   (ANSWER).

Q3 not done.