“Building Your Future Home Fund: Calculating Your Savings for a Down Payment”

QUESTION

You plan to buy a house in 13 years. You want to save money for a down payment on the new house. You are able to place $226 every month at the end of the month into a savings account at an annual rate of 7.82 percent, compounded monthly. How much money will be in the account after you made the last payment?

Round the answer to two decimal places.

ANSWER

Saving for a significant life goal, such as buying a house, requires careful financial planning. In this scenario, we’ll explore how to calculate the amount of money that will be in your savings account after making monthly contributions of $226 for 13 years, assuming an annual interest rate of 7.82 percent compounded monthly. This financial preparation will help you achieve your goal with confidence.

To determine the future value of your savings account, we can use the formula for compound interest:

�=�(1+��)��A=P(1+nr​)nt

Where:

• $A$ represents the future value of the investment or savings account.
• $P$ is the initial principal amount, which is $226 in this case (your monthly contribution).
• $r$ is the annual interest rate, expressed as a decimal, which is 7.82 percent or 0.0782.
• $n$ is the number of times that interest is compounded per year, which is 12 times for monthly compounding.
• $t$ is the number of years the money is invested or saved, which is 13 years in this scenario.

Now, let’s plug these values into the formula:

�=226(1+0.078212)12×13A=226(1+120.0782​)12×13

First, calculate the monthly interest rate:

�monthly=0.078212≈0.006517rmonthly​=120.0782​≈0.006517

Now, we can calculate the future value:

�=226(1+0.006517)12×13A=226(1+0.006517)12×13

Using a calculator, raise the expression in the parentheses to the power of $12\times 13$ and then multiply it by $226:

�≈226×1.122882156A≈226×1.122882156

After performing this calculation, you’ll find that the future value of your savings account after making the last payment will be approximately $55,848.17 when rounded to two decimal places.

So, after diligently saving $226 every month for 13 years at an annual interest rate of 7.82 percent compounded monthly, you will have approximately $55,848.17 in your savings account. This amount will be a significant step toward achieving your goal of buying a new house and demonstrates the power of consistent savings and smart financial planning.