Determining Rate Change in an Investment Question (1 Viewer)

[Jordhard]

I invest $8000 for 16 years & earn 2.4 times the original amount at 6% p.a. compounding quarterly (every 3 months). However after an unknown number of years during the 16 year period, the rate goes down by 0.5%. When did the rates change?

I have come up with the initial formula of:

2.4 = (1.015)^(4T) * (1.01375)^(64-4T)


However I cannot figure out how to determine T = ....

 

[braintic]

I invest $8000 for 16 years & triple my money at 6% compounding quarterly (every 3 months). After an unknown number of years the rate goes down by 0.5%. When did the rates change?

This question is not clear.
Are you saying that the money is invested for a certain period of time at 6% pa, and another period of time at 5.5% pa, with the two time periods adding to 16 years?
If so, the question doesn't work - even if the interest stays at 6%pa for the full 16 years, 1.015^64 is only 2.59 - you CAN'T triple your money.
Could you please clarify what you mean.

 

[Jordhard]

This question is not clear.
Are you saying that the money is invested for a certain period of time at 6% pa, and another period of time at 5.5% pa, with the two time periods adding to 16 years?

Yeah, sorry.

If so, the question doesn't work - even if the interest stays at 6%pa for the full 16 years, 1.015^64 is only 2.59 - you CAN'T triple your money.

Thank you, I've altered the question so that it works.

 

[braintic]

Are you asking how to do the question?
If so, I'll post a solution.

If you know how to do it and are setting it as a challenge question, I'll leave it for students to try.

 

[Jordhard]

Are you asking how to do the question?
If so, I'll post a solution.

If you know how to do it and are setting it as a challenge question, I'll leave it for students to try.

I'm asking how to do the question... I'm stumped on it haha

 

[braintic]

Here is the solution:
View attachment Financial.pdf

As you can see from the final answer, your choice of 2.4 was not ideal either - any lower and it would not have worked again (because 1.01375^64 is 2.396).

 

[Jordhard]

Here is the solution:
View attachment 32397

As you can see from the final answer, your choice of 2.4 was not ideal either - any lower and it would not have worked again (because 1.01375^64 is 2.396).

Thank you very much. Unfortunately my teacher wrote down an impossible number so I had to impend it. But I was more after seeing how to work out a question similiar to that. Again thank you

 

[braintic]

Thank you very much. Unfortunately my teacher wrote down an impossible number so I had to impend it. But I was more after seeing how to work out a question similiar to that. Again thank you

Hmmm - "impend" ??