Answer:
14.20669 years
Roughly 14 years and 2.5 months.
Step-by-step explanation:
Assuming this is compound interest.
The formula is [tex]A=P(1+\frac{r}{n})^{nt}[/tex]
[tex]A=[/tex] Final Amount
[tex]P=[/tex] Principal Amount
[tex]r=[/tex] Interest Rate
[tex]n=[/tex] # of times interest is compounded per year
[tex]t=[/tex] Time in years
We are looking for the times in years to double the money so
[tex]2500*2=5000[/tex]
[tex]A=5000[/tex]
[tex]P=2500[/tex]
[tex]r=0.05[/tex]
[tex]n=1[/tex]
[tex]t=?[/tex]
Lets solve for [tex]t[/tex] .
Step 1.
Plug in our numbers into the compound interest formula.
[tex]5000=2500(1+\frac{0.05}{1}) ^{1*t}[/tex]
Step 2.
Simplify the equation.
Evaluate [tex]1+\frac{0.05}{1}=1.05[/tex]
Evaluate [tex]1*t=t[/tex]
[tex]5000=2500(1.05) ^{t}[/tex]
Step 3.
Divide both sides of the equation by [tex]2500[/tex]
[tex]\frac{5000}{2500}=1.05 ^{t}[/tex]
Evaluate [tex]\frac{5000}{2500}=2[/tex]
[tex]2=1.05 ^{t}[/tex]
Step 4.
Take the natural log of both sides of the equation and rewrite the right side of the eqaution using properties of exponents/logarithms.
[tex]ln(2)=t*ln(1.05)[/tex]
Step 5.
Divide both sides of the equation by [tex]ln(1.05)[/tex]
[tex]\frac{ln(2)}{ln(1.05)}=t[/tex]
Step 6.
Evaluate
[tex]t=14.20669[/tex]
Roughly 14 years and 2.5 months.
