Una persona deposita 2,300 cada mes vencido en una cuenta de ahorro que le paga el 9.3% anual capitalizable cada mes.

¿Cuánto habrá ahorrado al cabo de cinco años? $

To determine how much a person will have saved after five years with monthly deposits into an account with compound interest, we will use the formula for the future value of an annuity. 

### Given dataTo determine how much a person will have saved after five years with monthly deposits into an account with compound interest, we will use the formula for the future value of an annuity. 

### Given 
- Monthly deposit ($ PMT $): 2,300
- Annual interest rate ($ r $): 9.3%
- Monthly interest rate: $ \frac{9.3\%}{12} = 0.775\% = 0.00775 $ (as a decimal)
- Number of years: 5
- Total periods ($ n $): $ 5 \times 12 = 60 $

### Formula
The future value of an annuity formula is:
\[
FV = PMT \times \left( \frac{(1 + r)^n - 1}{r} \right)
\]
Where:
- $ PMT $ is the monthly payment
- $ r $ is the monthly interest rate
- $ n $ is the total number of payments

Let's calculate the future value.The total amount saved after five years will be approximately $174,848.34.

Would you like more details or have any questions about the calculation?

Here are 5 related questions:
1. How would the savings change if the interest were compounded quarterly instead of monthly?
2. What would be the total interest earned in these five years?
3. How much would you need to deposit each month to reach a target savings amount of $200,000 in five years?
4. How would the total savings change if the interest rate increased to 10% annually?
5. What is the effect of changing the deposit frequency from monthly to bi-weekly?

**Tip:** Always ensure to differentiate between nominal interest rates (annual) and effective rates (monthly/quarterly) when calculating compound interest.

Una persona deposita 2,300 cada mes vencido en una cuenta de ahorro que le paga el 9.3% anual capitalizable cada mes. ¿Cuánto habrá ahorrado al cabo de cinco años?

Discover how much a person can save over five years by depositing 2,300 monthly into an account with a 9.3% annual interest rate, compounded monthly. This solution covers key concepts in compound interest and the future value of annuities, ideal for college-level or advanced high school students.

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