DE Poll

A CCCH has a 5,000 balance on a credit card that carries 12% annual interest rate. The CCCH is making the minimal monthly payments of 25. Determine after how many years the CCCH will have a balance of 1,000,000=$10^6$ on this credit card. Put your answer into DE-Poll using two decimals

The answer is $\approx 50$.

Solution Yearly payments are $25\times 12=300$ so we want to solve differential equation $B'=.12 B- 300$ with the initial condition $B(0)=5000$. WolframAlpha gives the formula $B(t)=2500 + 2500 e^{0.12 t}$. We want to solve equation $B(t)=10^6$ for $t$. WolframAlpha says $t=25/3 (\log(3) + \log(7) + \log(19))\approx 49.91$

One more?