Question

Of the following four types of savings account plans, which option would yield exponential growth of the money in the account?

• A. Each successive year, $2\%$ of the initial savings is added to the value of the account
• B. Each successive year, $1.5\%$ of the initial savings and 100$ is added to the value of the account
• C. Each successive year, $1$% of the current value is added to the value of the account
• D. Each successive year, 100$ is added to the value of the account

Answer 1

The correct option is C Each successive year, $1$% of the current value is added to the value of the account

Let $I$be the initial savings.

If each successive year, $1\%$ of the current value is added to the value of the account, then after $1$ year, the amount in the account will be $I+0.01I=I(1+0.01)$.

After $2$ years, the amount in the account will be $I(1+0.01)+0.01I(1+0.01)=(1+0.01)I(1+0.01)=I(1+0.01{)}^2$, and

After $t$ years, the amount in the account will be $I(1+0.01{)}^t$. This is exponential growth of the money in the account.