Question

if i put 500 dollars per month into a savings account that gains 4.5% in compound interest monthly, how much will i have in a year

Answer 1

To calculate the total amount in a savings account after one year with monthly deposits and compound interest, you can use the future value of a series formula, which is:

\[
FV = P \times \frac{(1 + r)^n - 1}{r}
\]

Where:
- \(FV\) is the future value of the investment/loan, including interest,
- \(P\) is the monthly deposit (in this case, $500),
- \(r\) is the monthly interest rate (annual rate divided by 12),
- \(n\) is the number of deposits (number of months).

Given:
- Monthly deposit, \(P = 500\)
- Annual interest rate = 4.5%, so monthly interest rate, \(r = \frac{4.5\%}{12} = \frac{0.045}{12} = 0.00375\)
- Number of months in a year, \(n = 12\)

Now, substituting the values into the formula:

\[
FV = 500 \times \frac{(1 + 0.00375)^{12} - 1}{0.00375}
\]

Calculating the expression inside the formula step by step:

1. \(1 + 0.00375 = 1.00375\)
2. \((1.00375)^{12} \approx 1.046047\)
3. \(1.046047 - 1 \approx 0.046047\)
4. \(\frac{0.046047}{0.00375} \approx 12.41256\)

Now plug this back into the future value formula:

\[
FV = 500 \times 12.41256 \approx 6206.28
\]

Therefore, after one year, you will have approximately **$6,206.28** in your savings account.