How much money would you need to invest now to obtain  
$
6
,
000
  in a CD account in  
19
  years if the interest in the CD is  
3.37
%
 , compounded monthly? (Round your answer to the nearest cent.)


To find how much money you need to invest now to obtain $6,000 in 19 years with an interest rate of 3.37%, compounded monthly, we can use the formula for compound interest:

\[
A = P \left(1 + \frac{r}{n}\right)^{nt}
\]

Where:
- $ A $ is the future value (in this case, $6,000).
- $ P $ is the present value (the amount to invest now).
- $ r $ is the annual interest rate (3.37% or 0.0337).
- $ n $ is the number of times the interest is compounded per year (monthly means $ n = 12 $).
- $ t $ is the time in years (19 years).

We are solving for $ P $, so rearrange the formula:

\[
P = \frac{A}{\left(1 + \frac{r}{n}\right)^{nt}}
\]

Now, plug in the given values:

\[
P = \frac{6000}{\left(1 + \frac{0.0337}{12}\right)^{12 \times 19}}
\]

First, calculate the terms inside the parentheses:

\[
1 + \frac{0.0337}{12} = 1 + 0.00280833 = 1.00280833
\]

Next, raise this to the power of $12 \times 19 = 228$:

\[
(1.00280833)^{228} \approx 1.978113
\]

Now divide the future value by this result:

\[
P = \frac{6000}{1.978113} \approx 3033.91
\]

Therefore, you would need to invest **$3,033.91** now to obtain $6,000 in 19 years with an interest rate of 3.37%, compounded monthly.

Would you like more details or have any questions?

### Related Questions:
1. What if the interest was compounded annually instead of monthly?
2. How does the future value change if the interest rate is higher?
3. What is the difference between simple and compound interest?
4. How would the required investment change for a shorter time period, like 10 years?
5. What would the future value be if you invested $3,500 instead of $3,033.91?

### Tip:
The more frequently interest is compounded, the more quickly your investment grows due to the effect of earning interest on interest.

How much money would you need to invest now to obtain $6,000 in a CD account in 19 years if the interest in the CD is 3.37%, compounded monthly? (Round your answer to the nearest cent.)

Learn how to calculate the initial investment required to reach $6,000 in 19 years in a CD account with a 3.37% interest rate, compounded monthly. This problem involves compound interest and exponential growth, and is suitable for Grades 10-12.

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