For the past 5 years, Frank and Peggy have deposited $15,000 in a retirement account with a simple interest rate of 7%. They plan to continue to make annual deposits for the next 20 years. Explain how their money will grow over time. Note: You do not need to extend their entire savings for 25 years in your explanation. Focus on the earning for the first several years and explain how their money will grow.
To understand how Frank and Peggy's money will grow over time, we need to calculate the interest earned on their annual deposits using the simple interest formula:
I = P * r * t
Where:
I = Interest earned
P = Principal amount (annual deposit)
r = Interest rate per period (in decimal form)
t = Number of periods (in this case, number of years)
In this case, Frank and Peggy deposit $15,000 annually, and the interest rate is 7% (or 0.07) per year.
For the first year, their initial deposit of $15,000 will earn interest:
I = $15,000 * 0.07 * 1 = $1,050
So after the first year, their investment will be worth $16,050.
For the second year, their deposit of $15,000 will earn interest:
I = $15,000 * 0.07 * 1 = $1,050
Their existing investment from the previous year has also earned interest:
I = $16,050 * 0.07 * 1 = $1,123.50
So after the second year, their investment will be worth $33,223.50.
This process continues each year. For each subsequent year, the deposited amount of $15,000 will earn interest, and the existing investment will also earn interest.
By repeating this calculation for several years, you can observe how their money will grow. However, keep in mind that this calculation assumes simple interest and does not take into account compounding, which would result in even higher growth. To calculate the total savings after 25 years, you would continue this process and add up the accumulated amounts each year.