Question

A person invested dollar sign, 7, comma, 400$7,400 in an account growing at a rate allowing the money to double every 6 years. How much money would be in the account after 4 years, to the nearest dollar?

Answer 1

To find out how much money will be in the account after 4 years, we can use the doubling time of the investment. Since the money doubles every 6 years, we first need to determine the growth rate.

1. **Determine the growth factor for 6 years:**
\[
\text{Growth factor for 6 years} = 2
\]

2. **Calculate the growth factor for 1 year:**
To find the annual growth factor, we can use the formula:
\[
\text{Annual growth factor} = \sqrt[6]{2}
\]
Using a calculator, we find:
\[
\sqrt[6]{2} \approx 1.122462
\]

3. **Calculate the growth factor for 4 years:**
To find the growth factor for 4 years, we raise the annual growth factor to the power of 4:
\[
\text{Growth factor for 4 years} = (1.122462)^4
\]
Calculating this:
\[
(1.122462)^4 \approx 1.491825
\]

4. **Calculate the amount in the account after 4 years:**
Now we can find the amount in the account after 4 years by multiplying the initial investment by the growth factor for 4 years:
\[
\text{Amount after 4 years} = 7,400 \times 1.491825 \approx 11,030.00
\]

5. **Rounding to the nearest dollar:**
The amount in the account after 4 years, rounded to the nearest dollar, is:
\[
\boxed{11030}
\]