If $\$ 950$ are deposited into an account with $5 \%$ interest rate, compounded quarterly, what is the balance after 4 years?
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Round to the nearest cent.
Enter
Answer
Calculating the above expression gives the final balance after 4 years, rounded to the nearest cent, as \(\boxed{\$1,215.89}\).
Step 1 ：In the first quarter, the account earns \(\frac{0.05}{4}(\$950)\) in interest, so the balance is \(\$950 +\frac{0.05}{4}(\$950) = \left(1 + \frac{0.05}{4}\right)(\$950)\).
Step 2 ：Similarly, the value of the account is multiplied by \(1 + \frac{0.05}{4}\) each quarter.
Step 3 ：So after 4 years, which is \(4\cdot 4 = 16\) quarters, the balance is \[\left(1 + \frac{0.05}{4}\right)^{4\cdot 4}(\$950)\].
Step 4 ：Calculating the above expression gives the final balance after 4 years, rounded to the nearest cent, as \(\boxed{\$1,215.89}\).
