compound interest,
n. the interest accumulated over a given period at a given rate when each successive interest payment is aggregated with the principal sum for the purpose of calculating the next interest payment. For example, capital of $C invested at i% per annum compound yields
$C (1 + i /100)n
after n years. More generally, the interest on P units at i% compounded n times per period yields
P (1 + i /(100n))n
units at the end of the period, which is equivalent to receiving (i/n)% interest for n periods and reinvesting the principal. As the interest becomes instantaneous, with n tending to infinity, the sum approaches
P × exp(i /100).
See exponential function.
$C (1 + i /100)n
after n years. More generally, the interest on P units at i% compounded n times per period yields
P (1 + i /(100n))n
units at the end of the period, which is equivalent to receiving (i/n)% interest for n periods and reinvesting the principal. As the interest becomes instantaneous, with n tending to infinity, the sum approaches
P × exp(i /100).
See exponential function.