#### Determine the Required Savings to Reach a Financial Goal

https://www.youtube.com/embed/gBp3v-SVVyQ
Welcome to a lesson on calculating the regular savings amount required to achieve a financial goal. In this video, we’ll utilize the value of an annuity formula to guide us in reaching our financial goal through a systematic savings plan.
Let’s start by reviewing the formula used to determine the value of an annuity, denoted as A, for a given regular deposit amount, P. The formula is as follows:
A = P * ((r/n) / ((1 + r/n)^(n*t) – 1))
Our goal is to rearrange this formula to find the regular savings amount, P, needed to reach our financial goal, A. To do this, we’ll solve for P:
P = A / ((r/n) / ((1 + r/n)^(n*t) – 1))
Now that we have the formula to calculate P, let’s apply it to a practical example. Imagine you want to purchase a car in four years, aiming to pay for it in cash, with a determined cost of $15,500. You plan to make monthly deposits into an account that earns 6% interest, compounded monthly. What should your monthly deposits be, and how much interest will you earn over this period?
Using the formula, we calculate the monthly deposit amount:
P = 15,500 * ((0.06/12) / ((1 + 0.06/12)^(12*4) – 1))
After evaluating this expression, we find that you need to save approximately $286.52 per month to pay for the car in cash.
Next, let’s determine the interest earned over the four-year period. You will make this monthly deposit 12 times a year for four years, and this value represents the total amount deposited into the account. Therefore, to find the interest earned, subtract the total deposit amount from the ending account balance:
Interest = (Ending Account Balance) – (Total Deposit Amount) Interest = 15,500 – (286.52 * 12 * 4) Interest = $1,747.04
So, you would earn $1,747.04 in interest over this four-year period.
Now, let’s consider a scenario where you save for only two years, using the same formula but with t equal to 2 (instead of 4). We’ll calculate the monthly deposit amount and the interest earned over this two-year period.
P = 15,500 * ((0.06/12) / ((1 + 0.06/12)^(12*2) – 1))
Calculating this, we find that you need to save $609.47 per month for two years to pay for the car in cash.
Now, let’s determine the interest earned over the two-year period:
Interest = 15,500 – (609.47 * 12 * 2) Interest = $872.72
By saving for only two years, you would earn $872.72 in interest.
This example underscores the power of compounded interest. While saving for a longer period yields a higher interest amount and requires smaller monthly deposits, reducing the savings duration significantly increases the monthly deposit amount needed to reach the same financial goal.
In conclusion, these calculations emphasize the importance of considering time and interest rates when planning for financial goals, such as purchasing a car. The choice between saving for a longer duration with smaller monthly deposits or a shorter duration with larger monthly deposits can significantly impact your savings plan.

As found on YouTube
Florida RetirementPosted in Retire Wealthy, Retirement PlanningTagged annuity, Finance, financial, formula, goal, investment, james, math, monthly, reach, required, Savings, sousa