Use the compound-interest formula to find the account balance A, where P is principal, r is interest rate, n is the number of compounding periods per year, t is time in years, and [tex]$A$[/tex] is the account balance.
| P | r | compounded | t |
| --------- | ------- | ---------- | --- |
| $11,663 | 9.7 % | Daily | 3 |
The account balance is approximately $ [ ] .
(Simplify your answer. Do not round until the final answer. Then round to two decimal places as needed.)
Answer (2)
Substitute the given values into the compound interest formula: A = P ( 1 + n r ) n t .
Plug in the values: A = 11663 ( 1 + 365 0.097 ) ( 365 ) ( 3 ) .
Calculate the value of A: A ≈ 15601.75 .
The account balance is approximately $15601.75 .
Explanation
Understanding the Problem We are given the principal amount P = $11 , 663 , the annual interest rate r = 9.7% = 0.097 , the number of compounding periods per year n = 365 (daily), and the time in years t = 3 . We need to find the account balance A using the compound interest formula.
Applying the Formula The compound interest formula is given by: A = P ( 1 + n r ) n t We will substitute the given values into this formula.
Calculating the Account Balance Substituting the values, we get: A = 11663 ( 1 + 365 0.097 ) ( 365 ) ( 3 ) Now, we calculate the value of A.
Final Calculation and Rounding A = 11663 ( 1 + 365 0.097 ) 1095 A = 11663 ( 1 + 0.000265753 ) 1095 A = 11663 ( 1.000265753 ) 1095 A ≈ 11663 × 1.33765 A ≈ 15601.74516 Rounding to two decimal places, we get A ≈ 15601.75 .
Final Answer Therefore, the account balance after 3 years is approximately $15601.75 .
Examples
Compound interest is a powerful concept that applies to many real-world financial situations. For example, when you invest in a retirement account or a savings account, the interest earned is often compounded. Understanding how compound interest works can help you make informed decisions about your investments and savings. It can also apply to loans, where interest is charged on the outstanding balance, and the compounding effect can significantly increase the total amount you owe over time. Knowing how to calculate compound interest allows you to project the future value of your investments or the total cost of a loan.
The account balance after using the compound interest formula with the given values is approximately $15601.75. We calculated this by substituting the principal, interest rate, compounding periods, and time into the formula. The final result is rounded to two decimal places.
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