SOLUTION: How long would it take to double $2000 in the bank deposit with 4% interest compounded monthly

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Question 1197961: How long would it take to double $2000 in the bank deposit with 4% interest compounded monthly
Found 3 solutions by josgarithmetic, math_tutor2020, MathTherapy:
Answer by josgarithmetic(39614)   (Show Source):
You can put this solution on YOUR website!
If that 4% is annual rate then , x is in MONTHS. Solve for x.

Answer by math_tutor2020(3816)   (Show Source):
You can put this solution on YOUR website!

We'll be using the compound interest formula
A = P*(1+r/n)^(n*t)

The variables are
A = final amount after t years
P = deposit amount
r = annual interest rate in decimal form
n = number of times the money is compounded per year
t = number of years
In this case we know the following values:
A = 4000 (we want the deposit of 2000 to double to 4000)
P = 2000
r = 0.04
n = 12 (compounding 12 times a year; aka compounding monthly)
t = unknown, which we'll be solving for
If the variable is in the trees (aka exponent), then log it down.
In other words, we use logarithms to isolate the exponent.

A = P*(1+r/n)^(n*t)
4000 = 2000*(1+0.04/12)^(12*t)
4000/2000 = (1.003333)^(12*t)
2 = (1.003333)^(12*t)
log( 2 ) = log( (1.003333)^(12*t) ) .... apply logs to both sides
log( 2 ) = 12*t*Log( 1.003333 ) .... use the rule log(A^B) = B*log(A)
12*t*Log( 1.003333 ) = log( 2 )
t = log(2)/(12*log(1.003333))
t = 17.359278
This value is approximate.

A shortcut through use of estimation:
We can use the Rule of 72 to determine an approximate timeframe when the amount of money will double.
This is where we divide 72 over the whole number form of the interest rate. We treat "4%" as simply "4", so we have 72/4 = 18
The rule of 72 says we need about 18 years for the money to double. This is fairly close to the 17.359278 figure calculated earlier.

Answer: Approximately 17.359278 years

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Edit:
Be careful. The portion that the tutor @josgarithmetic wrote is not correct. This is because approximately, which you'll find is not equivalent to approximately.

It's not valid to say is the same as

Answer by MathTherapy(10549)   (Show Source):
You can put this solution on YOUR website!

How long would it take to double $2000 in the bank deposit with 4% interest compounded monthly

Since this refers to DOUBLING, the initial amount is never needed, as the formula is always: This gives us: ------ Substituting .04 for i (interest), and 12 for m (annual compounding periods) ----- Converting to LOGARITHMIC form Time it'll take to double, or However, since this investment is being compounded MONTHLY, you need to ROUND UP to the next month, which is month 5. So, correct answer should be 17 years, 5 months. A QUICKER method is to use the Rule of 69.3. This rule is MOST PRECISE for interest rates below 6%. From 6% - 10%, the MOST PRECISE is the Rule of 72. Depending on the interest rate, other rules (Rule of 70 & 78) can be used to get the most accurate time-estimate. Using the Rule of 69.3, we get: i (in percent form) * time (in years) = 69.3 4t = 69.3 ------- Substituting 4 for interest rate Time taken to double, or . See how precise the Rule of 69.3 is as a time-predictor?