To solve this, we use the Future Value of an Ordinary Annuity formula, which is suitable for calculating regular payments needed to reach a specific future goal with compounded interest:

$FV = P \cdot \frac{(1 + i)^n - 1}{i}$

Where:

• $FV$ is the future value (the goal) = $83,000$
• $P$ is the monthly payment (what we are solving for)
• $i$ is the monthly interest rate = annual rate ÷ 12 = $\frac{6\%}{12} = 0.005$
• $n$ is the total number of payments = months = $3 \times 12 = 36$

Rearranging the formula to solve for $P$:

$P = \frac{FV \cdot i}{(1 + i)^n - 1}$

Substituting the values:

$P = \frac{83,000 \cdot 0.005}{(1 + 0.005)^{36} - 1}$

Let me compute this for you.The monthly payments required to save $83,000 in 3 years with a 6% annual interest rate compounded monthly are approximately $2,110.02.

Would you like further explanation on the formula, alternative scenarios, or additional assistance?

Related Questions:

1. How would the required payment change if the interest rate were higher, say 8%?
2. What is the total amount of money the Jones will contribute over 3 years?
3. How much of the $83,000 goal is due to interest earned?
4. What if they only save for 2 years—how would their monthly payment change?
5. What is the balance after 2 years if they stick to these payments?

Tip:

Understanding how compounding frequency affects payments can help you make smarter financial decisions when saving or borrowing.