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?

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.