Question

Suppose you deposit $2500 in a savings account that pays you 5% interest per year. (Calculator)

Answer 1

Answer:

14.20669 years

Roughly 14 years and 2.5 months.

Step-by-step explanation:

Assuming this is compound interest.

The formula is $A=P(1+\frac{r}{n})^{nt}$

$A=$ Final Amount

$P=$ Principal Amount

$r=$ Interest Rate

$n=$ # of times interest is compounded per year

$t=$ Time in years

We are looking for the times in years to double the money so

$2500*2=5000$

$A=5000$

$P=2500$

$r=0.05$

$n=1$

$t=?$

Lets solve for $t$ .

Step 1.

Plug in our numbers into the compound interest formula.

$5000=2500(1+\frac{0.05}{1}) ^{1*t}$

Step 2.

Simplify the equation.

Evaluate $1+\frac{0.05}{1}=1.05$

Evaluate $1*t=t$

$5000=2500(1.05) ^{t}$

Step 3.

Divide both sides of the equation by $2500$

$\frac{5000}{2500}=1.05 ^{t}$

Evaluate $\frac{5000}{2500}=2$

$2=1.05 ^{t}$

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.

$ln(2)=t*ln(1.05)$

Step 5.

Divide both sides of the equation by $ln(1.05)$

$\frac{ln(2)}{ln(1.05)}=t$

Step 6.

Evaluate

$t=14.20669$

Roughly 14 years and 2.5 months.