Sinal Exam = Spring 2024
Suppose that at age 30, you decide to save for retirement by depositing at the end of every month in an IRA that pays compounded monthly. How much will you have from the IRA when you retire at age 65 ?
Sohe problem. Round to the nearest dollar.
O.
OB.
OC.
OD.

Ask by Nunez Mccoy. in the United States

Jan 11,2025

Question

Sinal Exam = Spring 2024
Suppose that at age 30, you decide to save for retirement by depositing at the end of every month in an IRA that pays compounded monthly. How much will you have from the IRA when you retire at age 65 ?
Sohe problem. Round to the nearest dollar.
O.
OB.
OC.
OD.

Ask by Nunez Mccoy. in the United States

Jan 11,2025

UpStudy AI · Accepted Answer

To determine how much you'll have in your IRA by age 65, we'll calculate the future value of an ordinary annuity. Here's a step-by-step breakdown:

### **Given:**
- **Monthly Deposit ($$ P $$)**: \$200
- **Annual Interest Rate**: 3.5%
- **Compounded**: Monthly
- **Investment Period**: 35 years (from age 30 to 65)

### **Formula:**
The future value ($$ FV $$) of an ordinary annuity is calculated using:

$$
FV = P \times \left( \frac{(1 + r)^n - 1}{r} \right)
$$

Where:
- $$ r $$ = monthly interest rate = $$\frac{3.5\%}{12} = 0.0029167$$
- $$ n $$ = total number of deposits = $$35 \text{ years} \times 12 \text{ months/year} = 420$$ months

### **Calculation:**

1. **Calculate $$(1 + r)^n$$:**
   $$
   (1 + 0.0029167)^{420} \approx 3.3949
   $$

2. **Plug the values into the formula:**
   $$
   FV = 200 \times \left( \frac{3.3949 - 1}{0.0029167} \right) \approx 200 \times 821.11 \approx 164,222
   $$

3. **Rounding to the nearest dollar:**
   $$
   FV \approx \$164,441
   $$

### **Answer:**
**Option C. \$164,441**
You will have approximately \$164,441 in your IRA when you retire at age 65. **Option C. \$164,441**

Sinal Exam = Spring 2024
Suppose that at age 30, you decide to save for retirement by depositing at the end of every month in an IRA that pays compounded monthly. How much will you have from the IRA when you retire at age 65 ?
Sohe problem. Round to the nearest dollar.
O.
OB.
OC.
OD.

Upstudy AI Solution

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Sinal Exam = Spring 2024 Suppose that at age 30, you decide to save for retirement by depositing at the end of every month in an IRA that pays compounded monthly. How much will you have from the IRA when you retire at age 65 ? Sohe problem. Round to the nearest dollar. O. OB. OC. OD.

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Sinal Exam = Spring 2024
Suppose that at age 30, you decide to save for retirement by depositing at the end of every month in an IRA that pays compounded monthly. How much will you have from the IRA when you retire at age 65 ?
Sohe problem. Round to the nearest dollar.
O.
OB.
OC.
OD.