1. Exam FM Problem 007 Learning Objective: “Annuities”
Wisconsin Center of Actuarial Excellence Technology Enhanced Learning Project
Exam FM Problem 007
Learning Objective: “Annuities”
Welcome to the tutorial on exam FM. Today we are going to go over the problem 7, which is part of the learning objective “Annuities”. Here is the view of the problem.

2. Please choose one of the answers and submit it
Please choose one of the answers and submit it. If incorrect hit the grey ‘x’ in the top right to try again.

3. For this problem, we need to find the accumulated value of fund Y
For this problem, we need to find the accumulated value of fund Y. In order to get the AV we need the cash flow principal and interest into fund Y. To get the amount of interest, we first need to know the balance of fund X.
Now let’s look at the Fund X. We are given that the interest earned and a principle of 100 is withdrawn from the fund X at the end of each year.
If we consider interest only, the amount in Fund X stays the same because the interest was subtracted.
So the balance of fund X start with 1000 at time 0, and decrease by 100 every year considering the 100 principal withdrawn.

4. For fund Y, the principal and interest earned in fund X was deposited at end of year. To calculate the AV of fund Y, we need to find the AV of principle and AV of interest.
The AV of Principle is just 100 times S angle 10. The formula is (1+i)^n minus1 over i. Plug in the number we get AV principle
The interest into fund Y at time 1 is just the balance of Fund X at time 0 times the interest rate for fund X. Notice the i is .06 here, which is different from the interest rate for fund Y. The AV Interest is a decreasing annuity, which equals 100*.06 * Ds angle ten. The symbol Ds angle n represents the AV of an annuity that pays n at time 1, n-1 at time 2 and decrease by 1 every year.

6. For fund Y, the principal and interest earned in fund X was deposited at end of year. To calculate the AV of fund Y, we need to find the AV of principle and AV of interest.
The AV of Principle is just 100 times S angle 10. The formula is (1+i)^n minus1 over i. Plug in the number we get AV principle
The interest into fund Y at time 1 is just the balance of Fund X at time 0 times the interest rate for fund X. Notice the i is .06 here, which is different from the interest rate for fund Y. The AV Interest is a decreasing annuity, which equals 100*.06 * Ds angle ten. The symbol Ds angle n represents the AV of an annuity that pays n at time 1, n-1 at time 2 and decrease by 1 every year.

7. For fund Y, the principal and interest earned in fund X was deposited at end of year. To calculate the AV of fund Y, we need to find the AV of principle and AV of interest.
The AV of Principle is just 100 times S angle 10. The formula is (1+i)^n minus1 over i. Plug in the number we get AV principle
The interest into fund Y at time 1 is just the balance of Fund X at time 0 times the interest rate for fund X. Notice the i is .06 here, which is different from the interest rate for fund Y. The AV Interest is a decreasing annuity, which equals 100*.06 * Ds angle ten. The symbol Ds angle n represents the AV of an annuity that pays n at time 1, n-1 at time 2 and decrease by 1 every year.

8. Thanks for watching. Questions. Comments
Thanks for watching! Questions? Comments? Please us at: Funding provided by the Society of Actuaries and the Wisconsin School of Business Voice: Ting Xia Faculty Supervisor: EW(Jed) Frees
That’s the end of this tutorial. Thanks for watching!