A $7 million deposit earns 5 percent for 9 years. If the account loses 2 percent per year after that, how long will it take to be reduced back to $7 million?

Question

Quizplus · Accepted Answer

The initial deposit grows to $11,376,357.97 (found using the compound interest formula A=P(1+r/n)^(nt), where P=7,000,000, r=0.05, n=1, and t=9). 
Then, the account loses 2% per year, which means it is reduced to 98% of its previous value each year. 
Let t be the number of years it takes for the account to be reduced back to $7,000,000. 
Then, (0.98)^t * $11,376,357.97 = $7,000,000. 
Solving for t gives t = 21.74 years, so the answer is D.

A $7 Million Deposit Earns 5 Percent for 9 Years