Final answer:
To find the balance, interest earned, and effective rate of interest for Reese's bank account, the compound interest formula is applied. The calculations yield a final balance of $1422.56, interest earned of $271.56, and an effective rate of 5.4901%. None of the given options match these calculations exactly, indicating a need for a closer review of the answer choices.
Step-by-step explanation:
The question requires applying the formula for compound interest to calculate the future balance of a bank account, the interest earned, and the effective rate of interest. To solve this question, we will use the formula:
A = P(1 + \(\frac{r}{n}\))^nt
Where:
- A is the amount of money accumulated after n years, including interest.
- P is the principal amount (the initial amount of money).
- r is the annual interest rate (decimal).
- n is the number of times that interest is compounded per year.
- t is the time the money is invested or borrowed for, in years.
Using the given values:
- P = $1151.00
- r = 5.4%, which is 0.054 in decimal form
- n = 12 (since the interest is compounded monthly)
- t = 4 years
The balance (A) at the end of 4 years can be calculated as follows:
A = 1151(1 + \(\frac{0.054}{12}\))^(12\times4)
When you solve this, A = \$1422.56 (rounded to the nearest cent).
The amount of interest earned is the final balance minus the initial deposit:
Interest Earned = A - P = $1422.56 - $1151.00 = $271.56
The effective rate of interest can be found by:
Effective Rate = (A/P)^(1/t) - 1
Plugging in our values:
Effective Rate = (1422.56/1151)^(1/4) - 1
Which gives us an effective rate of 0.054901 or 5.4901%.
So the correct option from the list is:
a) $1422.56, b) $271.56, c) 5.4901%
However, note that none of the given options perfectly match the calculated values, so the most accurate representation of the answer is the computed figures, and not the options provided.