Question: Arjun will save money by making 6 quarterly deposits of $900 in an account which pays 7.3% interest. How much will he has in the account after making these deposits? Round your answer to the nearest cent.
1. **State the problem:** Arjun makes 6 quarterly deposits of $900 each into an account with an annual interest rate of 7.3%. We want to find the total amount in the account after all deposits.
2. **Identify the formula:** Since deposits are made quarterly and interest is compounded quarterly, we use the future value of an ordinary annuity formula:
$$ A = P \times \frac{(1 + r)^n - 1}{r} $$
where:
- $A$ is the amount accumulated after $n$ deposits,
- $P$ is the deposit amount per period,
- $r$ is the interest rate per period,
- $n$ is the number of deposits.
3. **Calculate the interest rate per quarter:**
Annual interest rate = 7.3% = 0.073
Quarterly interest rate $r = \frac{0.073}{4} = 0.01825$
4. **Plug in the values:**
$P = 900$
$n = 6$
$$ A = 900 \times \frac{(1 + 0.01825)^6 - 1}{0.01825} $$
5. **Calculate $(1 + r)^n$:**
$$ (1 + 0.01825)^6 = 1.01825^6 \approx 1.1143 $$
6. **Calculate numerator:**
$$ 1.1143 - 1 = 0.1143 $$
7. **Calculate fraction:**
$$ \frac{0.1143}{0.01825} \approx 6.2630 $$
8. **Calculate total amount:**
$$ A = 900 \times 6.2630 = 5636.7 $$
9. **Round to nearest cent:**
$5636.70$
**Final answer:** Arjun will have approximately $5636.70$ in the account after making 6 quarterly deposits.