Question

You deposit 2500 dollars into an account that pays 3.5% interest compounded monthly. what is the balance after 3 years?​

Answer 1

Answer:

$2776.35

Step-by-step explanation:

To calculate the future balance of an investment compounded monthly, we can use the compound interest formula:

$\sf A = P \left(1 + \dfrac{r}{n}\right)^{nt}$

where:

• $\sf A$ is the future balance,
• $\sf P$ is the principal amount (initial deposit),
• $\sf r$ is the annual interest rate (as a decimal),
• $\sf n$ is the number of times interest is compounded per year, and
• $\sf t$ is the number of years.

In this case:

• $\sf P = \ 2500$,
• $\sf r = 0.035$ (3.5% expressed as a decimal),
• $\sf n = 12$ (compounded monthly), and
• $\sf t = 3$ years.

Substitute these values into the formula:

$\sf A = 2500 \left(1 + \dfrac{0.035}{12}\right)^{12 \times 3}$

Now, calculate the future balance:

$\sf A \approx 2500 \left(1 + \dfrac{0.002916666667}{1}\right)^{36}$

$\sf A \approx 2500 \left(1.002916667 \right)^{36}$

$\sf A \approx 2500 \times 1.110540876$

$\sf A \approx 2776.352189$

$\sf A \approx 2776.35 \textsf{{in 2 d.p.)}$

Therefore, the balance after 3 years will be approximately $2776.35.

Answer 2

Final answer:

To find the balance after 3 years, we use the formula for compound interest. Plug in the given values and calculate the expression to find the balance is approximately $2758.68.

Explanation:

To calculate the balance after 3 years, we can use the formula for compound interest: A = P(1+r/n)^(nt)

Where:

• A is the final amount
• P is the principal amount (initial deposit)
• r is the annual interest rate (as a decimal)
• n is the number of times interest is compounded per year
• t is the number of years

In this case, P = $2500, r = 0.035 (3.5% as a decimal), n = 12 (compounded monthly), and t = 3. Plugging these values into the formula, we get:

A = 2500(1+0.035/12)^(12*3)

Calculating this expression, the balance after 3 years is approximately $2758.68.