A bank account is growing by 4.3 % per year. Find the doubling time.

Round your answer to the nearest integer.

Can someone explain how to solve this step by step. I have been stuck on this for quite a while

1.043^n = 2

n log 1.043 = log 2

n = log 2/log 1.043 = 16.5 years

you want 1.043^t = 2.0

t log 1.043 = log 2
t = log2/log1.043 = 16.5 years

This is roughly in accordance with the rule of 72: 72/4.3 = 16.7

To find the doubling time of a bank account growing by a certain rate, you can use the formula:

Doubling Time = ln(2) / (ln(1 + r))

where r is the annual growth rate expressed as a decimal.

Step 1: Convert the growth rate to a decimal.
The growth rate is given as 4.3%, so divide it by 100 to convert it to decimal form:
r = 4.3% ÷ 100 = 0.043

Step 2: Plug the growth rate into the formula.
Doubling Time = ln(2) / (ln(1 + 0.043))

Step 3: Evaluate the natural logarithms.
Use a calculator to find the natural logarithms of 2 and 1 + 0.043:
Doubling Time ≈ 0.693 / 0.0422

Step 4: Divide to find the doubling time.
Divide the value of ln(2) by the value of ln(1 + 0.043):
Doubling Time ≈ 16.40

Step 5: Round your answer to the nearest integer.
Since the question asks to round to the nearest integer, the doubling time is approximately 16 years.

So, the doubling time for the bank account growing by 4.3% per year is approximately 16 years.

To find the doubling time of a bank account growing at a certain annual percentage rate (APR), we can use the rule of 72. The rule of 72 is a simple mathematical formula that helps estimate how long it takes for an investment to double in value.

Step 1: Determine the value of "n" using the rule of 72.
The rule of 72 states that the number of years it takes for an investment to double is approximately equal to 72 divided by the annual percentage growth rate. In this case, the bank account is growing by 4.3% per year.

Using the formula, n = 72 / APR, we find:
n = 72 / 4.3
n ≈ 16.744

Step 2: Round the value of "n" to the nearest whole number.
In the question, it is mentioned to round the answer to the nearest integer. Since "n" is approximately 16.744, rounding it gives us 17.

Therefore, the doubling time for the bank account is approximately 17 years.