P=100(n/m)^(1/6)-1

Question

If the final balance was $670.05 and the interest rate was 5%, please reconstruct the amount of the initial investment. (Note: because of the way this formula is set up, we use "5" for percentage P, not "0.05". Also, for your check, remember that the 6th root is the (1/6) power.)

Answer 1

P=P0(1+r)^n is the formula for compound interest, where r=rate (=0.05), P0 the initial amount, P (=$670.05) the accumulated amount, and n the number of time periods.

Growth=P/P0=670.05/P0=1.05^n. P0=670.05/1.05^n. If n=6 P0=670.05/1.05^6=$500.