# Actuarial Discussion Forum - Professional Discussions for Professional Actuaries

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1. ## Question Meaning

A 30-yr loan of 1000 is repaid with payments at the end of each year.

Each of the first ten payments equals the amount of interest due. Each of the next ten payments equals 150% of the amount og interest due. Each of the last ten payments is X.

effective rate of 10%

Calculate X

My Question 1:
I cannot get the meaning of "Each of the first ten payments equals the amount of interest due. Each of the next ten payments equals 150% of the amount of interest due. "

My Question 2:
Actually, I always misunderstand the question meaning! Sometimes, I know how to answer the question if I know the question well. Do you guys have any suggestion?

Thank you!

2. Question 1.

During the initial 10 years, interest due at the end of year of the 1000 loan is 1000*10%=100. So annual payment during the initial 10 years at year end is 100 and amount of loan outstanding remains 1000 since no principal has been paid off. Actually, after you acquire some level of proficiency during your study, you could skip this part and jump directly into solving the second and third 10-year periods as the loan amount is the same before and after this period of time. All you need to determine is the size of annual interest payment is 100 = 1000*10% for the second part.

During the second 10 years, annual payment each year at year end = 100*150%= 150. Therefore FV at the end of the second 10 years is -203.12877 (by inputting N=10, I/Y=10, PV=1000, PMT=-150, then <CPT> <FV>). "-ve" sign means balance is a loan i.e. still owing money.

During the last 10 years, PV=203.12877 (sign changed), (N=10, I/Y=10 unchanged), FV=0, press <CPT> <PMT>, answer is -33.05827188.

Question 2.

Just allow more time for practice and observe the key words that you might have missed in your initial grasp of the problem. Part of the test is to translate a verbal problem into an algebraic form that is readily solvable. It takes time. More drill will help. It is just a phase of learning that we normally have to go through. Persevere.

Hope it helps.

What is the answer for this question?

A 30-yr loan of 1000 is repaid with payments at the end of each year.

Each of the first ten payments equals the amount of interest due. Each of the next ten payments equals 150% of the amount og interest due. Each of the last ten payments is X.

effective rate of 10%

Calculate X

My Question 1:
I cannot get the meaning of "Each of the first ten payments equals the amount of interest due. Each of the next ten payments equals 150% of the amount of interest due. "

My Question 2:
Actually, I always misunderstand the question meaning! Sometimes, I know how to answer the question if I know the question well. Do you guys have any suggestion?

Thank you!
Originally Posted by luther
Question 1.

During the initial 10 years, interest due at the end of year of the 1000 loan is 1000*10%=100. So annual payment during the initial 10 years at year end is 100 and amount of loan outstanding remains 1000 since no principal has been paid off. Actually, after you acquire some level of proficiency during your study, you could skip this part and jump directly into solving the second and third 10-year periods as the loan amount is the same before and after this period of time. All you need to determine is the size of annual interest payment is 100 = 1000*10% for the second part.

During the second 10 years, annual payment each year at year end = 100*150%= 150. Therefore FV at the end of the second 10 years is -203.12877 (by inputting N=10, I/Y=10, PV=1000, PMT=-150, then <CPT> <FV>). "-ve" sign means balance is a loan i.e. still owing money.

During the last 10 years, PV=203.12877 (sign changed), (N=10, I/Y=10 unchanged), FV=0, press <CPT> <PMT>, answer is -33.05827188.

Question 2.

Just allow more time for practice and observe the key words that you might have missed in your initial grasp of the problem. Part of the test is to translate a verbal problem into an algebraic form that is readily solvable. It takes time. More drill will help. It is just a phase of learning that we normally have to go through. Persevere.

Hope it helps.

I saw your profile you guys are in HK, how's the market over there? Are you guys working or still in school?

thanks

5. I am working in a life insurer but not yet in the actuarial department. I started my self study of actuarial exams after May this year when I finished my LOMA exams. In this sense, I am a beginner and just passed Exam P this summer.

Market is still very good for experienced professionals with around 7 years experience but entry positions are becoming limited in Hong Kong. About 1-2 years ago, all actuarial graduates got offers readily from insurers. But not now. Some moved to the investment field and some to teaching posts. They still get jobs easily as the entry requirements for the actuarial programme in HKU are the highest in town. They are indeed the cream.

Openings in China are expected to increase sharply but local people get local pay and that's real competition. Many experienced professionals from Hong Kong work in China and they do get international pay. If you are interested to come over, just contact the recruitment consultants and they should have their contacts and much more solid advice to give. Perhaps talk more to you on this after Exam FM this Wednesday.

Answer from me has been given in my previous post. Not sure what the "official" answer is. I could be wrong. In that case, just let me know as I am only a student in this field.

6. Originally Posted by luther
Question 1.

During the initial 10 years, interest due at the end of year of the 1000 loan is 1000*10%=100. So annual payment during the initial 10 years at year end is 100 and amount of loan outstanding remains 1000 since no principal has been paid off. Actually, after you acquire some level of proficiency during your study, you could skip this part and jump directly into solving the second and third 10-year periods as the loan amount is the same before and after this period of time. All you need to determine is the size of annual interest payment is 100 = 1000*10% for the second part.

During the second 10 years, annual payment each year at year end = 100*150%= 150. Therefore FV at the end of the second 10 years is -203.12877 (by inputting N=10, I/Y=10, PV=1000, PMT=-150, then <CPT> <FV>). "-ve" sign means balance is a loan i.e. still owing money.

During the last 10 years, PV=203.12877 (sign changed), (N=10, I/Y=10 unchanged), FV=0, press <CPT> <PMT>, answer is -33.05827188.

Question 2.

Just allow more time for practice and observe the key words that you might have missed in your initial grasp of the problem. Part of the test is to translate a verbal problem into an algebraic form that is readily solvable. It takes time. More drill will help. It is just a phase of learning that we normally have to go through. Persevere.

Hope it helps.

Won't the amount of interest due each year decrease as you pay principal? I don't think the payments are level on this one.

7. Originally Posted by mreevit
Won't the amount of interest due each year decrease as you pay principal? I don't think the payments are level on this one.
Could you show me how you would solve this problem?

8. As previously stated the first 10 payments are just interest, therefore after ten years \$1000 of principal still remain.

Now for the tricky part, you have to notice the pattern in how much principal is left after each 150% of interest payment. As stated before this is not going to be level payment. Let Pn = Principal remaining after the nth 150% of interest payment. Then you get:

P1= 1000(1.1)-1000(.1)(1.5)=1000(.95)
P2=1000(.95)(1.1) - 1000(.95)(.1)(1.5)= 1000(.95)^2

Using this pattern you will get

P10=1000(.95)^10=598.74

Now you get to solve for X. Using the equation X *(a-angle-10-10%)=598.74
You will get X=97.44.

Hope this helps....if not I could try to explain further.

9. Brilliant! Thanks a million. A nice one indeed.

10. Originally Posted by DMB3401
As previously stated the first 10 payments are just interest, therefore after ten years \$1000 of principal still remain.

Now for the tricky part, you have to notice the pattern in how much principal is left after each 150% of interest payment. As stated before this is not going to be level payment. Let Pn = Principal remaining after the nth 150% of interest payment. Then you get:

P1= 1000(1.1)-1000(.1)(1.5)=1000(.95)
P2=1000(.95)(1.1) - 1000(.95)(.1)(1.5)= 1000(.95)^2

Using this pattern you will get

P10=1000(.95)^10=598.74

Now you get to solve for X. Using the equation X *(a-angle-10-10%)=598.74
You will get X=97.44.

Hope this helps....if not I could try to explain further.
That's exactly what I meant!!! Good work!

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