In August 2013, Ally Bank was offering 0.16% interest on its Online Savings Account, with interest reinvested daily. Assuming that this rate of return continued for 8 years, how much was would a deposit of $4000 in August 2013 be worth in August 2021? (round to the nearest cent)
To calculate the future value of a deposit with compound interest over time, we can use the formula:
Future Value = Principal x (1 + Interest Rate)^Time
Where:
- Principal is the initial deposit amount ($4000 in this case)
- Interest Rate is the annual interest rate divided by the number of compounding periods per year (0.16% daily, meaning approximately 0.0016 divided by 365 days)
- Time is the number of years (8 years in this case)
Let's plug in the values to calculate the future value:
Principal = $4000
Interest Rate = 0.0016 / 365 = 0.00000438356 (rounded)
Time = 8 years
Future Value = $4000 x (1 + 0.00000438356)^8
To calculate this expression, let's break it down into steps:
Step 1: Calculate (1 + 0.00000438356)
(1 + 0.00000438356) ≈ 1.00000438356
Step 2: Calculate (1.00000438356)^8
(1.00000438356)^8 ≈ 1.00003493693
Finally, multiply the Principal by the result to get the Future Value:
Future Value ≈ $4000 x 1.00003493693
The approximate Future Value of a $4000 deposit in August 2013, with a 0.16% interest rate reinvested daily for 8 years, would be about $4000.14.
Please note that this calculation assumes constant 0.16% interest rate and daily compounding, and the actual interest calculated by the bank may vary slightly due to compounding methods and any rate changes over the years.
figure the number of days, t
Then the result would be 4000(1 + 0.0016/365)^t