Question

At the beginning of evey month, maggie invests 150 in an account that pays a 6 nnual rate of interest. How much money will there be in the account after six years?.

Answer 1

The final amount in her account will be approximately $2733.90.

Step-by-step explanation:

To calculate the amount of money in Maggie's account after six years, we can use the formula for compound interest:

`P = P0(1 + r)^n`

where:
P is the final amount
P0 is the initial investment
r is the annual interest rate
n is the number of years

In this case, Maggie invests $150 at the beginning of each month, so her initial investment is $150 * 12 = $1800. The annual interest rate is 6% or 0.06, and she invests for 6 years, or 6 * 12 = 72 months.

Using the formula, we can calculate the final amount:

`P = $1800(1 + 0.06/12)^72`

= $2733.90

Therefore, there will be approximately $2733.90 in Maggie's account after six years.

Answer 2

To calculate the amount of money in the account after six years, we can use the formula for compound interest. Maggie invests $150 at the beginning of every month for six years at a 6% annual interest rate. After calculating using the formula, we find that the amount of money in the account after six years is approximately $1199.94.

Step-by-step explanation:

To determine how much money will be in an account after six years when investing $150 every month at an annual interest rate of 6%, we need to use the formula for the future value of a series of annuities. Since the investments are made at the beginning of each month, and the interest rate is annual, we'll convert the annual interest rate to a monthly rate by dividing it by 12. Furthermore, we need to account for the effect of compound interest.

The future value of an annuity formula when contributions are made at the beginning of each period (known as an annuity due) is:

FV = P × ·[ (1 + r)ⁿ⁻¹] / r + P

Where:

• P = monthly investment
• r = monthly interest rate (annual rate / 12)
• n = total number of payments (years × 12)

Let's calculate it step by step:

1. Convert the annual rate to a monthly rate: r = 6% / 12 = 0.5%
2. Calculate the number of payments: n = 6 years × 12 months/year = 72
3. Use the future value formula for annuities due with these values:

FV = 150 × ·[ (1 + 0.005)⁷² - 1] / 0.005 + 150

= $1199.94.