Geometric
Compound Interest
Example
Sara invested $1,000 in a savings account paying 4% interest compounded annually. Determine the amount of money Sara will have in the account at the end of the first five years.
Step 1. Determine the amount of money in the account after 1 year.
A 1 = 1000 + (.04)(1000)=1000 + 40= $1040
Step 2. Determine the amount of money in the account after 2 years.
A 2 = 1040 + (.04)(1040) = 1040 + 41.60 = $1081.60
Step 3. Use the pattern to determine the amount of money in the account after 3, 4, and 5 years.
A 3 = 1081.60 + (.04)(1081.60)=1081.60 + 43.26= $1124.86
A 4 = 1124.86 + (.04)(1124.86)=1124.86 + 44.99= $1169.85
A 5 = 1169.85 + (.04)(1169.85)=1169.85 + 46.79= $1216.64
A 4 = 1124.86 + (.04)(1124.86)=1124.86 + 44.99= $1169.85
A 5 = 1169.85 + (.04)(1169.85)=1169.85 + 46.79= $1216.64
Step 4. Create a geometric sequence to show the amount of money in the account after each of the 5 years.
1040, 1081.60, 1124.86, 1169.85, 1216.64
Step 5. Determine a1 and r for the sequence.
a 1 = 1040 and r = 1.04
Step 6 . Write an explicit formula for the geometric sequence.
an = 1040(1.04)n-1 or an= 1000(1.04) n
Notice this is the same formula used for compound interest in the Exponentials Unit. A = P(1 + r)t