Question

Lauren plans to deposit $9000 into a bank account at the beginning of next month and $200/month into the same account at the end of that month and at the end of each subsequent month for the next 7 years. If her bank pays interest at a rate of 4%/year compounded monthly, how much will Lauren have in her account at the end of 7 years

Answer 1

Lauren will have approximately $17,122.62 in her account at the end of 7 years.

Step-by-step explanation:

To calculate the future value of the account, we can use the formula for compound interest: A = P(1 + r/n)^(nt), where:

• A = the future value of the account
• P = the initial deposit
• r = the annual interest rate (as a decimal)
• n = the number of times the interest is compounded per year
• t = the number of years

In this case, Lauren plans to deposit $9000 at the beginning and $200 at the end of each subsequent month, for a total of 84 deposits (7 years * 12 months).

Therefore, the future value can be calculated as follows:

A = 9000(1 + 0.04/12)^(12*7) + 200(1 + 0.04/12)((1 + 0.04/12)^(12*7) - 1)/(0.04/12)

Simplifying the equation gives us

A ≈ $17,122.62

Answer 2

The answer is "$ 30614.427"

Step-by-step explanation:

Given value:

`P = \$ \ 9000\\\\r= 4 \% \ \ = (0.04)/(12) \ = 0.003\\\\n= 12 \\\\t= 7\\\\ a= \$ \ 200`

Formula:

`Future\ value = P * (1+(r)/(n))^(nt-1) + a ( \frac{1+{(r)/(n)}^(nt) -1}{(r)/(n)})`

`= 9000 * (1+0.003)^(12 * 7-1) + 200 ( \frac{(1+{0.003}^(12 * 7)) -1}{0.003}) \\\\ = 9000 * (1.003)^(84-1) + 200 ( \frac{{1.003}^(84) -1}{0.003})\\\\ = 9000 * (1.003)^(83) + 200 ( \frac{{1.003}^(84) -1}{0.003})\\\\ = 9000 * 1.28226397 + 200 ( (1.28611077 -1)/(0.003))\\\\ = 11,540.3757 + 200 ( (0.28611077)/(0.003))\\\\ = 11,540.3757 + 200 * 95.3702567\\\\= 11,540.3757 + 19,074.0513\\\\=30614.427`