Question

Compare the accumulated values at the end of 10 years if P100 is invested at the rate of 12% per year compounded annually, semi-annually, quarterly, monthly, daily, and continuously.

Answer 1

Amount = 100

Interest rate = 12 %

Time = 10 years

Future value = Amount * (1 + R/n)^{^(n*t)}

    Annual Compounding: FV = 100 x (1 + (12% / 1))^ (1 x 10)

= 100 x (1 + 0.12)^ (10)  

= 310.58 $

    Semi-Annual Compounding: FV = 100 x (1 + (12% / 2))^ (2 x 10)

= 100 x (1 + 0.06)^ (20)

= 100 x 3.2071354722128447318829929845779

= 320.71 $

    Quarterly Compounding: FV = 100 x (1 + (12% / 4))^ (4 x 10)

= 326.20 $

    Monthly Compounding: FV = 100 x (1 + (12% / 12))^ (12 x 10)

= 330.04 $

    Daily Compounding: FV = 100 x (1 + (12% / 365))^ (365 x 10)

= 331.95 $

    Continuous Compounding: FV = 100 x 2.7183^(12% x 10)

= 332.01 $