You will deposit $3000 in a bank account at a 2% interest compounded monthly. The formula for
compound interest is shown below:
A(t) = P(1 + r/n)^(nt)
a. Select the value of P, r and n from the problem statement.
b. Explain the order in which you will perform the operations to calculate A(t).
c. What will be the amount in the bank account after 4 years?
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a.
- P = $3000 (the initial deposit)
- r = 2% = 0.02 (interest rate)
- n = 12 (compounded monthly)
b. To calculate A(t), we will perform the operations in the following order:
1. Calculate the bracketed term (1 + r/n):
(1 + 0.02/12) = 1.00166667
2. Raise this term to the power of nt:
(1.00166667)^(12*4) = (1.00166667)^48
3. Multiply this by the initial deposit P:
$3000 * (1.00166667)^48
c. To find the amount in the bank account after 4 years, we plug in the values:
A(4) = $3000 * (1.00166667)^48
A(4) = $3000 * 1.103817108
A(4) = $3311.45
Therefore, the amount in the bank account after 4 years will be approximately $3311.45.
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