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Compute the amount earned on $80,000 invested at 3.26% APR in one year if compounding is taking place daily. (Round your answer to the nearest cent.)

a) $2,540.00
b) $2,600.00
c) $2,700.00
d) $2,800.00

User Manishie
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1 Answer

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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).

User Tim McJilton
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