Assume we invest $2000 for one year in a savings account that pays an APR (Annual Percentage Rate) of 10% compounded quarterly.
The compound interest formula is: Balance after t periods = Principal × (1 + r)t
The final balance using the compound interest formula is $______.
To find the final balance using the compound interest formula, we need to substitute the given values into the formula.
Principal (P) = $2000
Annual interest rate (r) = 10% = 0.10
Number of compounding periods per year (n) = 4 (since interest is compounded quarterly)
Time (t) = 1 year
Now let's substitute these values into the compound interest formula:
Balance after t periods = Principal × (1 + r)^t
= $2000 × (1 + 0.10/4)^(4 × 1)
= $2000 × (1 + 0.025)^4
= $2000 × (1.025)^4
= $2000 × 1.103812890625
≈ $2207.63
Therefore, the final balance using the compound interest formula is approximately $2207.63