Jacob invested $500 in a stock and after a year had $596. what was Jacobs rate of return?
1 answer:
Answer:
Jacob's rate of return is <u>19.2%</u>.
Step-by-step explanation:
Given:
Jacob invested $500 in a stock and after a year had $596.
Now, to find the rate of return.
So, we get the amount of return first:
Present value - value before a year = Return.
$596 - $500 = $96.
Now, to get the rate:
Return / Value before a year × 100.
Therefore, Jacob's rate of return is 19.2%.
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This is a compound interest problem, therefore s(t) should be in the form:
where:
t = time in years
s(t) = the value of your item after t years
a = the initial value of your item
r = rate
Therefore, we already know that a = 245$.
Now, we can calculate r:
![r = \sqrt[t]{ \frac{s}{a} }](https://tex.z-dn.net/?f=r%20%3D%20%20%5Csqrt%5Bt%5D%7B%20%5Cfrac%7Bs%7D%7Ba%7D%20%7D%20)
![r = \sqrt[5]{ \frac{560.50}{245} }](https://tex.z-dn.net/?f=r%20%3D%20%5Csqrt%5B5%5D%7B%20%5Cfrac%7B560.50%7D%7B245%7D%20%7D%20)
= 1.18
Therefore, the correct answers are a = 245 and r = 1.18
where:
t = time in years
s(t) = the value of your item after t years
a = the initial value of your item
r = rate
Therefore, we already know that a = 245$.
Now, we can calculate r:
= 1.18
Therefore, the correct answers are a = 245 and r = 1.18