Question

Calvin deposits $400 in a savings account that accrues 5% interest compounded monthly. after c years, calvin has $658.80. makayla deposits $300 in a different savings account that accrues 6% interest compounded quarterly. after m years, makayla has $613.04. what is the approximate difference in the number of years that calvin and makayla have their money invested?

Answer 1

Answer:

Makayla invests her money 2 years longer.

Step-by-step explanation:

Answer 2

You will need a special formula to compute this.
Years = log (total/principal) / [n * log * (1 + rate / n)]

Part A) Calvin $400 5% monthly 658.80 Time = ?
Monthly compounding "n" = 12
Years = log(658.80/400) / [12 * log(1+ (.05/n))
Years = log ( 1.647 ) / (12 * log ( 1.0041666667 )
Years = 0.21669359917 / 12 * 0.0018058008777
Years = 0.21669359917 / 0.0216696105
Years = 9.999884362


Part B) Makayla 300 6% quarterly  613.04Time=?
Quarterly compounding
n = 4
Years = log (total/principal) / [n * log * (1 + rate / n)]
Years = log (613.04/300) / [4 * log (1 + .06/4)]
Years = log ( 2.0434666667 ) / 4 * log (1.015)
Years = 0.31036755784 / 4 * 0.0064660422492
Years = 0.31036755784 / 0.025864169
Years = 11.9999044949

So, the difference is roughly 3 years.