Suppose you deposited $30,000 in a bank account that pays 5.25% with daily compounding based on a 360-day year. How much would there be in the account after 8 months, assuming each month has 30 days? Select the correct answer. a. $31,080.11 b. $31,074.31 c. $31,056.91 d. $31,068.51 e. $31,062.71
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To calculate the future value of the deposit with daily compounding, we can use the formula for compound interest:
A = P × (1+ r / n) n×t
Where:
A is the future value of the investment/amount in the account after time t
P is the principal amount (initial deposit) = $30,000
r is the annual interest rate = 5.25% or 0.0525
n is the number of times the interest is compounded per year (daily compounding here based on a 360-day year)
t is the time the money is invested for (8 months or 8/12 years)
Given that the interest is compounded daily based on a 360-day year, the number of compounding periods (n) per year would be 360.
Let's calculate the future value after 8 months:
t = 8/12
t = 2/3
A = 30,000 x (1+ 0.0525 / 360 ) 360 x 2/3
Now, solving this equation gives:
A = 30,000 × (1+0.00014583333) 240
A = 30,000×1.035178603
A = 31,055.3581
Rounded to two decimal places, the amount in the account after 8 months would be approximately $31,055.36. None of the provided options match this exactly, but the closest one is c. $31,056.91.