Compount Interest Formula (With Contributions):

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FORMULA 1 (Future Value of Initial Investment):

A1 = P(1 + ^r⁄_n)^nt

FORMULA 2 (Future Value of Contributions):

A2 = PMT{[(1 + ^r⁄_n)^nt - 1] / ^r⁄_n}

FINAL FORMULA:

A = A1 + A2

Where:

• A = Future Balance
• P = Principal (Initial Investment)
• r = Interest Rate (as a %)
• t = Number of years
• n = Number of times interest is Compounded per year
• PMT = Contribution Amount

NOTE: These formulas assume the contribution frequency is equal to the number of times interest is compounded per year, and the contributions are made at the END of each time period.

Example Problem:

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We deposit an initial investment of $10,000 and make $500 monthly contributions.

If our investment time horizon is 10 years and expect a 6% rate of return (compounded monthly), what will be the final balance of our investment?

• P = $10,000
• r = 6% (0.06)
• t = 10 years
• n = 12 (compounded monthly = 12 times per year)
• PMT = $500

A = A1 + A2

A = P(1 + ^r⁄_n)^nt + PMT{[(1 + ^r⁄_n)^nt - 1] / ^r⁄_n}

A = (10000 X (1 + ^0.06⁄₁₂)^{(12 X 10)}) + (500 X {[(1 + ^0.06⁄₁₂)^{(12 X 10)} - 1] / ^0.06⁄₁₂})

A = (10000 X (1.005)^{(12 X 10)}) + (500 X {[(1.005)^{(12 X 10)} - 1] / 0.005})

A = (10000 X (1.005)¹²⁰) + (500 X {[(1.005)¹²⁰ - 1] / 0.005})

A = (18193.97) + (500 X (0.819396734 / 0.005))

A = (18193.97) + (500 X 163.8793468)

A = 18193.97 + 81939.67

A = 100133.64

The final balance of our investment will be $100,133.64.