Final answer:
To find out how much will be saved after 8 years with a weekly deposit of $25 into an account with a 14% APR, we calculate the future value of an ordinary annuity. Using the formula for future value and considering the weekly deposits, we can determine the total amount saved, including interest compounded annually.
Step-by-step explanation:
Given the scenario, we are looking to calculate the final amount in an account with compounded interest at an annual percentage rate (APR) of 14% where $25 is saved weekly for the last 8 years. Since the question does not specify that interest is compounded weekly or continuously, we will use the simple approach where contributions are made at the end of each period and interest is compounded annually.
To solve this, we need to calculate the future value of an ordinary annuity because $25 is being deposited at the end of each week. Here's the formula:
Future Value of Annuity = P * [(1 + r)^nt - 1] / r
Where,
P = Periodic payment ($25)
r = Periodic interest rate (14% per year or 0.14)
n = Number of times the interest is compounded per year (1 for annual)
t = Number of years (8)
However, since our payments are weekly, we also need to find the equivalent annual rate for weekly payments. Let's use the future value formula for an ordinary annuity:
Total savings = $25 * [(1 + 0.14/52)^(52*8) - 1] / (0.14/52) = Approximate value after calculation
Using a calculator or financial software, you would follow the steps to calculate the future value with the parameters provided. The calculation should give you the total amount saved, including interest.