1% Growth weekly on investment

Briancody

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I challenged my son to make 1% growth weekly on a original $30 investment. I calculated that over 23 years it would reach $1 mil. I track this weekly after 14 weeks he has reached 3 years 10 weeks into the plan. One of my questions is what is the yearly interest rate if the weekly rate is 1%.
 
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I challenged my son to make 1% growth weekly on a original $30 investment. I calculated that over 23 years it would reach $1 mil. I track this weekly after 14 weeks he has reached 3 years 10 weeks into the plan. One of my questions is what is the yearly interest rate if the daily rate is 1%.

You have not asked a sufficient question.

1% * 365 = 365%

(1 + 1%)^(365) - 1 = 3678%

There are other variations. It really depends on what it is you actually mean.
 
Thank You for the response

I meant 1% weekly compounded weekly. Trying to figure out what the yearly interest rate would be. So That I can write a simple formula to recalculate at the end of the first 52 weeks.
 
I challenged my son to make 1% growth weekly on a original $30 investment. I calculated that over 23 years it would reach $1 mil. I track this weekly after 14 weeks he has reached 3 years 10 weeks into the plan. One of my questions is what is the yearly interest rate if the weekly rate is 1%.

I see you quietly edited this, changing "daily" to "weekly" in the last line, as I expected you meant.

But do you see the ambiguity that is still present? There are several ways to state interest rates.

But let's assume that each week the amount grows by 1%. How much will it have grown in a year?

Each week it is multiplied by 101%, that is, 1.01. After 52 weeks, it has grown by 1.0152 = 1.678, which means 67.8% annual interest (in some sense). Continuing to compound for 23 years, we have 1.67823 = 147,354. That times $30 gives $4,420,631. But this number is highly sensitive to small changes; for example, I didn't take into account that a year is not exactly 52 weeks, and I didn't round.

There are other questions to be asked, but I'll leave that for others to do.
 
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