Answer:
The rate of simple interest is 9%
Explanation:
* Lets talk about the simple interest
- The simple Interest Equation (Principal + Interest) is:
A = P(1 + rt) , Where
# A = Total amount (principal + interest)
# P = Principal amount
# I = Interest amount
# r = Rate of Interest per year in decimal r = R/100
# R = Rate of Interest per year as a percent R = r * 100
# t = Time period involved in months or years
- The rule of the simple interest is I = Prt
* lets solve the problem
- Charles deposited $12,000
∴ P = $12,000
- He withdrew $5,000 from his account after one year
- He receives a total amount of $9,340 after 3 years
∴ A = $9340 and t = 3
- Lets find the inetrest after 1 year
∵ I = Prt
∵ P = 12000
∵ t = 1
∴ I = 12000(r)(1) = 12000r
- Lets subtract the money that he withdrew
∵ He withdrew $5000
∵ He deposit at first 12000
∴ He has after the withdrew 12000 - 5000 = 7000
- The new P for the next 2 years is 7000
- This amount will take the same rate r for another two years
- The total money is $9340
∵ I = A - P
∵ A = 9340
∵ P = 7000
∴ The amount of interest = 9340 - 7000 = 2340
- The amount of interest after 3 years is 2340
- Lets find the amount of interest in the two years
∴ I = 7000(r × 2) = 14000r
- The amount of interest after the 3 years is the sum of the interest in
the 1st year and the other 2 years
∴ 2340 = 14000r + 12000r
∴ 2340 = 26000r ⇒ divide both sides bu 2340
∴ r = 2340 ÷ 26000 = 0.09
∵ The rate R in percentage = r × 100
∴ R = 0.09 × 100 = 9%
∴ The rate of simple interest is 9%