the table shows the value of a savings bond that doubles in value after 5 years. savings bond value\n| time…

the table shows the value of a savings bond that doubles in value after 5 years. savings bond value\n| time since purchase (years) | value (dollars) |\n| ---- | ---- |\n| 1 | 57.50 |\n| 2 | 66.13 |\n| 3 | 76.04 |\n| 4 | 87.45 |\n| 5 | 100.57 | which statement describes the bond? the bond has an original value of $57.70 and grows at a rate of 15%. the bond has an original value of $57.50 and grows at a rate of 85%. the bond had an original value of $50 and grows at a rate of 15%. the bond has an original value of $50 and grows at a rate of 85%.

the table shows the value of a savings bond that doubles in value after 5 years. savings bond value\n| time since purchase (years) | value (dollars) |\n| ---- | ---- |\n| 1 | 57.50 |\n| 2 | 66.13 |\n| 3 | 76.04 |\n| 4 | 87.45 |\n| 5 | 100.57 | which statement describes the bond? the bond has an original value of $57.70 and grows at a rate of 15%. the bond has an original value of $57.50 and grows at a rate of 85%. the bond had an original value of $50 and grows at a rate of 15%. the bond has an original value of $50 and grows at a rate of 85%.

Answer

Answer:

C. The bond had an original value of $50 and grows at a rate of 15%.

Explanation:

Step1: Recall compound - growth formula

$A = P(1 + r)^t$, where $A$ is the final amount, $P$ is the principal (original) amount, $r$ is the annual interest rate, and $t$ is the number of years.

Step2: Test option C for $t = 1$

Let $P=50$ and $r = 0.15$. When $t = 1$, $A=P(1 + r)^1=50\times(1 + 0.15)=50\times1.15 = 57.50$.

Step3: Test option C for $t = 5$

When $t = 5$, $A = P(1 + r)^5=50\times(1 + 0.15)^5=50\times1.15^5=50\times2.0113571875\approx100.57$. So the bond had an original value of $50$ and grows at a rate of 15%.