You can earn .54 percent per month at your bank. If you deposit , how long must you wait until your account has grown
?
Note: Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16 .
Number of months

Question

You can earn .54 percent per month at your bank. If you deposit

, how long must you wait until your account has grown

?
Note: Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16 .
Number of months

UpStudy AI · Accepted Answer

To find out how long you need to wait until your account has grown to $6,700, we can use the formula for compound interest:

$$ A = P(1 + r)^n $$

where:
- $$ A $$ is the final amount ($6,700),
- $$ P $$ is the principal amount ($3,700),
- $$ r $$ is the monthly interest rate (0.54% or 0.0054),
- $$ n $$ is the number of months.

We need to solve for $$ n $$ when $$ A = \$6,700 $$ and $$ P = \$3,700 $$.

Substitute the values into the formula:

$$ 6700 = 3700(1 + 0.0054)^n $$

Now, we can solve for $$ n $$ using logarithms:

$$ \log(6700) = \log(3700) + n \cdot \log(1 + 0.0054) $$

$$ n = \frac{\log(6700) - \log(3700)}{\log(1 + 0.0054)} $$

Let's calculate the value of $$ n $$ using logarithms.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{\log_{10}{\left(6700\right)}-\log_{10}{\left(3700\right)}}{\log_{10}{\left(1+0.0054\right)}}$$
- step1: Add the numbers:
  $$\frac{\log_{10}{\left(6700\right)}-\log_{10}{\left(3700\right)}}{\log_{10}{\left(1.0054\right)}}$$
- step2: Convert the expressions:
  $$\frac{\log_{10}{\left(6700\right)}-\log_{10}{\left(3700\right)}}{\log_{10}{\left(\frac{5027}{5000}\right)}}$$
- step3: Subtract the terms:
  $$\frac{\log_{10}{\left(\frac{67}{37}\right)}}{\log_{10}{\left(\frac{5027}{5000}\right)}}$$
- step4: Use the logarithm base change rule:
  $$\log_{\frac{5027}{5000}}{\left(\frac{67}{37}\right)}$$
- step5: Rewrite the expression:
  $$\log_{\frac{5027}{5000}}{\left(67\right)}-\log_{\frac{5027}{5000}}{\left(37\right)}$$
The number of months it will take for your account to grow to $6,700 is approximately 110.25 months.
It will take approximately 110.25 months for your account to grow to $6,700.

You can earn .54 percent per month at your bank. If you deposit , how long must you wait until your account has grown
?
Note: Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16 .
Number of months

Upstudy AI Solution

Answer

Solution

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Latest Arithmetic Questions

You can earn .54 percent per month at your bank. If you deposit , how long must you wait until your account has grown ? Note: Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16 . Number of months

Upstudy AI Solution

Answer

Solution

Mind Expander

Related Questions

Latest Arithmetic Questions

You can earn .54 percent per month at your bank. If you deposit , how long must you wait until your account has grown
?
Note: Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16 .
Number of months