A person invests $$ 100$ , which earns interest that is compounded yearly.
This graph represents the value of this investment over time.
Approximately how many years does it take for the investment to double in value?
2 years 12 years
14 years 200 years

Answer

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Answer

$It takes approximately 14 years for the investment to double in value.$

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Step 1 ：Given the initial investment (P) is $100 a n d w e w a n t t o f i n d o u t w h e n i t d o u b l e s, s o t h e f u t u r e v a l u e (A) i s$ 200. We assume a reasonable interest rate of 5% (0.05) and the interest is compounded yearly (n=1).

Step 2 ：Use the formula for compound interest: $A = P (1 + \frac{r}{n})^{n t}$

Step 3 ：Plug in the values: $200 = 100 (1 + \frac{0.05}{1})^{1 * t}$

Step 4 ：Solve for t: $t = \frac{\log \frac{200}{100}}{\log 1.05} \approx 14.21$

Step 5 ： $It takes approximately 14 years for the investment to double in value.$

A person invests $100, which earns interest that is compounded yearly.This graph represents the value of this investment over time.Approximately how many years does it take for the investment to double in value?2 years 12 years14 years 200 years

Answer

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A person invests $$ 100$ , which earns interest that is compounded yearly.
This graph represents the value of this investment over time.
Approximately how many years does it take for the investment to double in value?
2 years 12 years
14 years 200 years