If x dollars is deposited every four weeks (13 times a year) into an account paying an annual interest rate r, expressed in decimal form, then the amount An in the account after n years can be approximated by the formula .If $45 is deposited every four weeks into an account paying 9% interest, approximate the amount in the account after 10 years.
To approximate the amount in the account after 10 years, we can use the formula An = P * (1 + r/n)^(n*t) where:
- P is the amount deposited every four weeks, which is $45 in this case.
- r is the annual interest rate, which is 9% expressed as 0.09 in decimal form.
- n is the number of times interest is compounded per year, which is 13 times (every four weeks).
- t is the number of years, which is 10 in this case.
Using these values in the formula, we can calculate the approximate amount in the account after 10 years:
An = $45 * (1 + 0.09/13)^(13*10)
First, let's simplify the exponent:
An = $45 * (1 + 0.006923)^130
Next, let's calculate the value inside the parentheses:
An = $45 * (1.006923)^130
Finally, let's calculate the approximate amount in the account after 10 years using a calculator or a scientific calculator function:
An ≈ $45 * 2.177999
An ≈ $97.81
Therefore, the approximate amount in the account after 10 years is approximately $97.81.