Question

If $6,000 is invested at 6% per year compounded monthly, the future value S at any time t (in months) is given by S=6,000(1.005) ^t. What is the amount after 1 year?

Answer 1

To find the amount after 1 year, substitute t with 12 in the formula S=6,000(1.005)^t. The amount will be $6,370.07.

Step-by-step explanation:

To find the amount after 1 year, we need to substitute t with 12 in the formula S=6,000(1.005)^t. So, S = 6,000(1.005)^(12).

Calculating this gives us S = 6,000(1.061678) = $6,370.07.

Therefore, after 1 year, the amount will be $6,370.07.

Answer 2

After 1 year, the amount of the investment compounded monthly at a rate of 6% would be $6,358.36.

Step-by-step explanation:

The formula for compound interest is given by
`\( S = P * (1 + r/n)^(nt) \)`, where:

- S is the future value of the investment/loan, including interest.

- P is the principal amount (initial investment).

- r is the annual interest rate (in decimal form).

- n is the number of times that interest is compounded per year.

- t is the time the money is invested/borrowed for, in years.

In this case, P = $6,000, r = 6\% = 0.06, n = 12 (compounded monthly), and t = 1 year.

Plugging these values into the compound interest formula, we get:

`\[ S = 6000 * \left(1 + (0.06)/(12)\right)^(12 * 1) \]`

Simplifying this expression gives the future value after 1 year:

`\[ S = 6000 * (1.005)^(12) \approx 6358.36 \]`

Therefore, after 1 year, the amount of the investment compounded monthly at a rate of 6% would be $6,358.36.