Erica's parents gave her $500 for her high school graduation. She put the money into a savings account that earned 7.5% annual interest. She left the money in the account for nine months before she withdrew it. How much interest did the account earn if the interest is paid monthly? About how many years and months would she have to leave the money in the account if she wants to reach her goal of saving $750?

$528.8385

5 years and 6 months

Step-by-step explanation:

The formula used to calculate compound interest is:

P = Po * (1+r)^t

Where P is the final value, Po is the inicial value, r is the rate and t is the amount of time.

In this case, we have Po = 500, r = 7.5% = 0.075. As the interest is paid monthly, we need a rate in month, so we have r = 0.075/12. So, we have that:

P = 500 * (1+0.075/12)^t

For the time of 9 months, we have:

P = 500 * (1+0.075/12)^9 = $528.8385

To save a total of $750, we can find the time t:

750 = 500 * (1.00625)^t

1.00625^t = 1.5

log(1.00625^t) = log(1.5)

t*log(1.00625) = 0.4055

t = 0.4055 / log(1.00625) = 0.4055 / 0.0062 = 65.4032 months

Rounding up (because we need to reach the goal of $750), 65.4032 months is equal to 5 years and 6 months

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step-by-step explanation: