What is the total amount in an account that has had $45 per month added into it for 30 years and grew with an annual interest rate of 8%?
To calculate the total amount in the account, we need to use the formula for compound interest.
First, we calculate the interest rate per period by dividing the annual interest rate by the number of compounding periods per year. In this case, the compounding is not specified, so we will assume it is compounded monthly (12 times a year). So the interest rate per month is 8% / 12 = 0.08 / 12 = 0.00666667.
Next, we calculate the total number of compounding periods over the 30-year period of the account. Since the account received monthly contributions, we multiply 30 years by 12 months per year, resulting in 30 * 12 = 360 compounding periods.
Now, we can use the formula for compound interest: A = P(1 + r/n)^(nt), where:
- A is the total amount in the account
- P is the initial amount (starting balance)
- r is the interest rate per period
- n is the number of compounding periods per year
- t is the number of years
In this case, P is $0 (starting balance), r is 0.00666667 (interest rate per month), n is 12 (compounding periods per year), and t is 30 (number of years).
To calculate the total amount, A, we substitute the values into the formula:
A = 0(1 + 0.00666667/12)^(12*30)
Since the starting balance is $0, the formula simplifies to:
A = (1 + 0.00666667/12)^(12*30)
To evaluate this expression, we can use a calculator or spreadsheet software.
Calculating the expression above, the total amount in the account after 30 years will be approximately $44,407.42.