Question

5. An insurance agent is trying to sell you an immediate retirement annuity, which for a lump-sum fee paid today will provide you with $50,000 every year for the next 20 years. You currently earn 8 percent annual return on investments with comparable risk to the retirement annuity. What is the most you would pay for this annuity?

6. You need $300,000 to buy a house. You decide to borrow money from the bank to finance your mortgage. Assume that the bank charges a fixed annual interest rate of 4.50 percent and the term of the loan is 30 years. If you are required to make an equal payment every year for 30 years to pay off the loan, what is the annual payment? (Note that banks typically require monthly mortgage payments. For this problem, however, let’s assume for simplicity that annual payments can be made.)

7. Your financial objective is to have $3,000,000 upon your retirement 40 years from now. If you have committed to make an equal annual deposit into an investment account that provides 9 percent annual return, how much will the annual deposit be?

8. If you invest $30,000 a year, every year in an account that earns 8 percent annual return, how long will it take for the balance in the account to reach $2,000,000?

Answer 1

(5) The most you would pay for this annuity = $490,907.50

Formula ;

Present Value of Annuity = PMT x 1 - [ { 1 / (1 + r)n } / r ]

Where;

PMT = Dollar amount of each annuity payment

r = Interest rate

n = number of periods in which payment will be made

Therefore;

Present Value of Annuity = 50000 x [1 - ( 1 / 1.08)20 / 0.08]

Present Value of Annuity = 50000 x [ (1 - 0.214548) / 0.08]

Present Value of Annuity = (50000 x 0.785452) / 0.08

Present Value of Annuity = 39272.60 / 0.08

Present Value of Annuity = $490,907.50