How it’s calculated
With monthly compounding and a deposit at the end of each month:
r = annual rate ÷ 12 ÷ 100 n = years × 12
Future value = P0 × (1 + r)^n + deposit × ((1 + r)^n − 1) ÷ r
Future value = P0 × (1 + r)^n + deposit × ((1 + r)^n − 1) ÷ r
For quarterly or yearly compounding, interest builds up every month on the credited balance and is added every 3 or 12 months.
Worked example
Start with $5,000, add $200 a month, 8% a year, 10 years
r = 0.006667 n = 120 (1 + r)^120 = 2.2196
5,000 × 2.2196 = $11,098
200 × (2.2196 − 1) ÷ 0.006667 = $36,589
Future value = $47,687
Deposits = $29,000 Interest earned = $18,687
r = 0.006667 n = 120 (1 + r)^120 = 2.2196
5,000 × 2.2196 = $11,098
200 × (2.2196 − 1) ÷ 0.006667 = $36,589
Future value = $47,687
Deposits = $29,000 Interest earned = $18,687
Adding $100 more each month grows the same plan to $65,982.
From paying interest to earning it
If you just finished paying off a $300-a-month debt, keep “paying” that $300 into savings. The habit is already built, and now compounding works for you instead of your lender.
