Question

How long (in years) would $500 have to be invested at 7%, compounded continuously, to amount to $905? (Round your answer to the nearest whole number.)

Answer 1

The formula for continuous compounding interest is

A = P(e^rt )

where

P = the Principal, which is the same as the starting amount = $500

A = the AFTER amount, which is the same as the ending amount = $905

r = the rate expressed as a decimal, 0.07

t = the number of years it takes for the Principal to become the

AFTER amount. That's the unknown that we want to find.

e = 2.718281828459

So we substitute

A = P(e^rt )

905 = 500(e)^0.07t

Divide both sides by 500

905 / 500 = (e)^0.07t

1.81 = (e)^0.07t

The exponential formula A = e^B is equivalent to B = ln(A).

similarly

0.07t = ln(1.81)

t =   ln(1.81) / 0.07 = 8.4760977896

t = 8.4 years