Question

michelle payne deposited $12,000 in a savings account paying 6.25% simple interest. how long (in years) will it take for her investment to amount to $21,000?

Explanation:

Step1: Identify simple interest formula

The simple interest formula for total amount is $A = P(1 + rt)$, where:

• $A$ = final amount, $P$ = principal, $r$ = annual interest rate, $t$ = time in years.

Step2: List given values

$A = 21000$, $P = 12000$, $r = 0.0625$ (converted from 6.25%)

Step3: Rearrange formula to solve for $t$

First divide both sides by $P$:
$\frac{A}{P} = 1 + rt$
Subtract 1 from both sides:
$\frac{A}{P} - 1 = rt$
Divide by $r$:
$t = \frac{\frac{A}{P} - 1}{r}$

Step4: Substitute values and calculate

First compute $\frac{A}{P}$:
$\frac{21000}{12000} = 1.75$
Then $\frac{A}{P} - 1 = 1.75 - 1 = 0.75$
Finally $t = \frac{0.75}{0.0625} = 12$

Answer:

12 years