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

the table shows the value of a savings bond that doubles in value after 5 years. savings bond value time since purchase (years) value (dollars) 1 57.50 2 66.13 3 76.04 4 87.45 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 time since purchase (years) value (dollars) 1 57.50 2 66.13 3 76.04 4 87.45 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:

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

Explanation:

Step1: Recall compound - interest formula

$A = P(1 + r)^t$, where $A$ is the final amount, $P$ is the principal (original amount), $r$ is the rate of growth, and $t$ is the time.

Step2: Check initial value

When $t = 1$, if $P = 50$ and $r=0.15$, then $A=P(1 + r)=50\times(1 + 0.15)=57.50$.

Step3: Check growth rate

For $t = 2$, $A = 50\times(1 + 0.15)^2=50\times1.3225 = 66.125\approx66.13$. For $t = 3$, $A = 50\times(1 + 0.15)^3=50\times1.520875 = 76.04375\approx76.04$. For $t = 4$, $A = 50\times(1 + 0.15)^4=50\times1.74900625 = 87.4503125\approx87.45$. For $t = 5$, $A = 50\times(1 + 0.15)^5=50\times2.0113571875 = 100.567859375\approx100.57$. So the bond had an original value of $50$ and grows at a rate of 15%.