Question

jake opened a savings account that earns 1.5% interest. jake estimates that, assuming he neither adds to or withdraws from his account, he will earn $240 in interest after 10 years. how much did jake deposit when he opened the account?

Explanation:

Step1: Recall simple interest formula

The simple interest formula is $I = P \times r \times t$, where $I$ = interest earned, $P$ = principal (initial deposit), $r$ = annual interest rate (decimal), $t$ = time in years.

Step2: Convert rate to decimal

$r = \frac{1.5\%}{100} = 0.015$

Step3: Rearrange formula to solve for $P$

$P = \frac{I}{r \times t}$

Step4: Substitute given values

$P = \frac{240}{0.015 \times 10}$

Step5: Calculate denominator and final $P$

$0.015 \times 10 = 0.15$
$P = \frac{240}{0.15} = 1600$

Answer:

$\$1600$