how many years will it take her money to grow to the $6,000 she needs for her small business start-up?

Question

Mia invests $2,500 in a money market account that earns 6% annual interest, compounded continuously. Approximately how many years will it take her money to grow to the $6,000 she needs for her small business start-up?

Step 1- Write the formula for continuously compounding interest and substitute the given values for the variables.

We are given Mia's principal investment in dollars, P, the annual interest rate, r, and the desired account balance in dollars, A. Be sure to write the 6% interest rate as the decimal 0.06. Substitute all the given values into the formula for continuously compounding interest, A = Pe^rt.

6,000=?

Note that the only variable in the resulting equation is t, which represents time in years.

Answer 1

A = Pe^rt

6,000 = 2,500(e)^6/100*t

6,000 = 2,500(e)^0.6t

6,000/2,500 = (e)^0.6t

2.4 = (e)^0.6t

Apply exponent rules

ln(2.4) = ln(e)^0.6t

ln(2.4) = 0.6t

0.87546 = 0.6t

t = 1.4591

t = 1.459 (rounded to hundredth place)