Final answer:
To find the compound interest for $80,000 at 3.26% APR compounded daily, use the formula A = P (1 + r/n)^(n*t). Substituting the given values and solving, the total accumulated amount is approximately $82,623.36. The interest earned, rounded to the nearest cent, is about $2,623.36.
Step-by-step explanation:
To compute the amount earned on $80,000 invested at 3.26% APR compounded daily for one year, we can use the compound interest formula:
A = P (1 + rac{r}{n})^{n*t}
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 for in years.
Substituting the given values into the formula, we get:
A = 80000 ( 1 + rac{0.0326}{365} )^{365*1}
Calculating the above expression gives us:
A = $80,000 ( 1 + 0.0000893 )^{365}
A ≈ $82,623.36
Therefore, the amount earned is the total amount accumulated minus the principal:
Interest Earned = $82,623.36 - $80,000 = $2,623.36
Rounding off to the nearest cent, the amount earned is approximately $2,623.36 (which is closest to option b).