If you make monthly payments of $312.00 into an ordinary annuity earning an annual interest rate of 6.2% compounded monthly, how much will you have in the account after 5 years? After 10 years?

To solve this, we use the **future value of an ordinary annuity formula**:

\[
FV = P \times \frac{(1 + r)^n - 1}{r}
\]

where:  
- $ FV $ = future value of the annuity  
- $ P $ = monthly payment = **312**  
- $ r $ = monthly interest rate = $ \frac{6.2\%}{12} = 0.062 / 12 = 0.005167 $  
- $ n $ = total number of payments = **years × 12**  

### **Step 1: After 5 years ($ n = 5 \times 12 = 60 $)**
\[
FV_{5} =

Learn how to calculate the future value of an ordinary annuity with monthly payments of $312 at an annual interest rate of 6.2% compounded monthly. This detailed solution shows the step-by-step process for finding the account balance after 5 and 10 years. Suitable for students in Grades 11-12 studying financial mathematics and compound interest.

Math Problem Statement

Solution

Step 1: After 5 years ( $n = 5 \times 12 = 60$ )

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