$100 is deposited at the beginning of every week for five years in an account that pays 14%/a, compounded weekly.
Find the future value of the annuity using the formula.
so, do you have the formula handy? what is it?
To find the future value of the annuity using the formula, you can use the following formula for compound interest:
Future Value = P * (1 + r/n)^(n*t)
Where:
P is the principal amount (the deposit made each week) which is $100
r is the annual interest rate which is 14% or 0.14
n is the number of times interest is compounded per year which is 52 (weekly)
t is the number of years which is 5
Substituting the values into the formula, we get:
Future Value = $100 * (1 + 0.14/52)^(52*5)
Now, let's calculate the future value step by step:
Step 1: First, calculate the value inside the parentheses:
1 + (0.14/52) = 1.0026923076923077
Step 2: Next, calculate the exponent:
52 * 5 = 260
Step 3: Finally, plug the calculated values back into the formula:
Future Value = $100 * (1.0026923076923077)^(260)
Using a calculator or a spreadsheet, calculate the value inside the parentheses and raise it to the power of 260:
(1.0026923076923077)^(260) = 1.938450862
Multiply this value by $100 to get the future value:
Future Value = $100 * 1.938450862 = $193.8450862
Therefore, the future value of the annuity is approximately $193.85.