Sam initially invested $4,500 into a savings account that offers an interest rate of 3% each year. He wants to determine the num ber of years, x, for which the account will have less than or equal to $7,020. Determine the solution set to the inequality that represents this situation.
2 answers:
Answer:
Principal = $4,500
Rate of interest=3%
Time = x years
We have to find number of years such that
Amount ≤$7020
Amount ≤ Principal + Simple interest
7020≤4500+ S.I
S.I≥7020-4500
S.I≥$2520
Formula for simple interest
S.I= , where P=Principal, R=Rate of interest, T=time
2520≥
x≤
So, the solution set is (0, ]
Answer:
The solution set to the given inequality : 0 < x ≤ 18.67
Step-by-step explanation:
Principal = $4500
Simple Interest Rate = 3%
= 0.03
Time = x year
Amount in the account will be less than or equal to $7020
⇒ Amount ≥ Principal × (1 + Rate × Time)
⇒ 7020 ≥ 4500(1 + 0.03·x)
⇒ 7020 ≥ 4500 + 135·x
⇒ 2520 ≥ 135·x
⇒ 18.67 ≥ x
The solution set to the given inequality : 0 < x ≤ 18.67
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