1. how does the age at which a person starts saving impact the amount they can earn in compound…

Explanation:

Step1: Recall compound - interest formula

The compound - interest formula is $A = P(1 + \frac{r}{n})^{nt}$, where $A$ is the amount of money accumulated after $n$ years, including interest, $P$ is the principal amount (the initial amount of money), $r$ is the annual interest rate (in decimal form), $n$ is the number of times that interest is compounded per year, and $t$ is the time the money is invested for in years.

Step2: Analyze the impact of starting - age on compound interest

If a person starts saving at a younger age, $t$ (the time of investment) is larger. For a fixed $P$, $r$, and $n$, as $t$ increases in the formula $A = P(1+\frac{r}{n})^{nt}$, the value of $(1 + \frac{r}{n})^{nt}$ increases, and thus $A$ (the final amount including compound interest) is larger.

Step3: Analyze the impact of low - interest rate on compounding

When the interest rate $r$ is low, the factor $(1+\frac{r}{n})$ is close to 1. As $t$ increases, the growth of $(1+\frac{r}{n})^{nt}$ is slower compared to a higher - interest rate. For example, if $r_1<r_2$, then for the same $P$, $n$, and $t$, $P(1 + \frac{r_1}{n})^{nt}<P(1+\frac{r_2}{n})^{nt}$. A low interest rate reduces the power of compounding as the growth of the investment over time is less significant.

Answer:

1. Starting to save at a younger age (larger $t$) leads to a larger amount of compound interest for a fixed principal, interest rate, and compounding frequency.
2. A low - interest rate reduces the power of compounding as the growth of the investment over time is less compared to a higher interest rate for the same principal, compounding frequency, and time period.