2. Suppose that you own real estate whose market value will be V(t) dollars t years from now on. 2-1) If the interest rate (r) remains constant over this period, t, what is the corresponding time stream of present value of the real estate you own? 2-2) What is the the optimal time to to sell your real estate given the time stream of present value? 2-3) Discuss the economic implications you learned from your answer to 2-2).

Assn #3 Pg 13 (1-10) And Works x em/?file=https://drive.google.com/uc?id%3D1CTEVTWK8MB4C_mgM7cZiHsSSPeOAZ 10&export%3Ddownload&filename%3DAttachment:%20PDF:%2 9. The balance in a bank account with an annual interest rate of 2%, compounded annually, can be represented using the function f(t) = 1000(1.02), where t is the time in years after opening the %3D 1 account. What was the approximate account balance 6 years and 3 months, or 6- years, after 4 the account was opened?

2. (2 pts) At an effective annual interest rate i, you are given: (a) the present value of an annuity-immediate with annual payments of 1 for n years is 40; and (b) the present value of an annuity-immediate with annual payments of 1 for 3n years is 70. Calculate the accumulated value of an annuity-immediate with annual payments of 1 for 2n years. Solution:

4. An insurer issues a 15-year annual premium-due endowment insurance of $100,000 benefit to life (50). The insurer charges an initial expenses of $ 1000 plus renewal expenses of 5% of each subsequent premium after the first premium payment. The premiums are made at the beginning of each year when (50) remains alive before reaching 70 and the benefit is paid at the end of K50 +1 years or when the person reaches the age 70 whichever occurs earlier. (a) Write down the gross future loss random variable L in terms of actuarial notations. (b) Calculate the gross premium-due G by using the Standard Select Survival Model with 5 % per year interest (Table D4) and the equivalence premium principle. 8 (c) Calculate the gross premium policy value V by using the equivalence premium G found in (b).

5. A bank account earns 5% interest compounded monthly. Suppose that $1000 is initially deposited into the account, but that $10 is withdrawn every month. (a) Show that the amount in the account after n-months is (1+) An-1 – 10, Ao = 1000. 0.05 12 An (b) How much money will be in the account after 1 year? (c) Suppose that instead of $10, a fixed amount d dollars is withdrawn each month. Find the value of d such that the amount in the account after each month remains $1000. (d) What happens if d is greater than this amount? (e) This problem deals with money and savings accounts. The concept behind this construction is much more general. Describe a further application, outside the realm of economics, where this model might be applied.

Solve the problem. 36) Suppose $14,000 is invested with 4% interest for 5 yr under the following compounding 36) options. Complete the table. Compounding Option n Value a. Daily b. Continuously A) B) C) D) Compounding Option n Value| 1 n/a a. Daily b. Continuously Compounding Option In Value| a. Daily b. Continuously Compounding Option In Value| 1 n/a a. Daily b. Continuously Result a. Daily b. Continuously Result $17,033.14 $17,783.62 Result 365 $17,099.45 n/a $17,783.62 Result $17,033.14 $17,099.64 Compounding Option In Value| Result 365 $17,099.45 n/a $17,099.64