Find n

[firemath]

Yes, I did say that n~12 is not correct. I said Is P ( 1+ .06/12)12*1= 2P? The answer is no. I tried using n=12 as the OP stated is the answer. I may be wrong but I never said that 12 was the answer.

I see. Thank you for the clarification!

 

[JeffM]

Dr Peterson, why would we not have to use the compound interest formula? If somehow the OP did, then how can that be. Isn't it true to know how many time the funds needs to be compounded depend on the number of years it is to take to double. What am I missing?

No It does not. Rates are usually specified in percents per year. Compounding periods are usually stated in periods per years. The number of periods, the exponent in the compound interest formulas, is usually found by multiplying years and compounding periods per year just as the periodic rate is found by dividing the annual percentage rate by the product of 100 and compounding periods per year.

The problem as given is not well specified. We are not explicitly told whether i is an annual rate or the periodic rate. If i is an annual rate, we are not told the number of compounding periods per year, which could be 1. We are not told whether we are to find the number of years or the number of periods, which may be the same thing if compounding occurs only once a year.

I have seldom seen a problem presented where it is more important to know EXACTLY what the original problem actually says. As stated, there is no possible way to know what is the correct answer.

 

[Dr.Peterson]

The question:
Use the compound interest formula to find n to the nearest larger integer value.

Given:
A = 2P; i = 0.06; n = ?

My work:
A = P(1 + i)ⁿ
2P = P(1 + 0.06)ⁿ
2 = (1 + 0.06)ⁿ

How do I solve for n in this case?

If the problem was given exactly as

Use the compound interest formula to find n to the nearest larger integer value.​

Given: A = 2P; i = 0.06; n = ?​

and if "the compound interest formula" as taught was exactly

A = P(1 + i)ⁿ​

then the answer is 12 (rounded, as required, up to the nearest integer).

We can check it:

A = P(1 + 0.06)¹² = 2.0122P, which is just a little over 2P​

The trouble is that "the compound interest formula" is written in many different ways, depending on the meaning of the variables involved. You didn't define any of the variables (such as whether the interest rate is annual, whether compounding is done annually, and whether n means a number of years or of compounding periods. Furthermore, the formula really is part of the question, and if you had stated it with the definitions of units, there would be no problem (though some people might complain about the way this was taught).

@Jomo assumed monthly compounding in writing i/12. @firemath saw a "t" in the problem that wasn't there, because they assumed a particular form of the formula. @frctl, you promised to post the exact problem; we really need it -- but, as I've indicated, we'll also need to see how "the formula" was taught.