Answer:
$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
