1.The value of an investment grows from R2200 to R3850 in 8 years. Determine the simple interest rate at which it was Invested.
2. James had R12000 and invested it for 5 years.If the value of his investment is R15600, what compound interest rate did it earn?
2200(1+8r)=3850
12000(1+r)^5 = 15600
just solve for r.
1. To calculate the simple interest rate, we can use the formula:
Simple Interest = Principal * Rate * Time
In this case, the principal (P) is R2200, the final amount (A) is R3850, and the time (T) is 8 years. We need to determine the rate (R).
First, let's calculate the simple interest earned during this period:
Interest = Final Amount - Principal
= R3850 - R2200
= R1650
Now we can substitute the values into the formula to find the interest rate:
Interest = Principal * Rate * Time
R1650 = R2200 * R * 8
To find the rate (R), rearrange the formula:
Rate = Interest / (Principal * Time)
R = R1650 / (R2200 * 8)
= 0.094
Therefore, the simple interest rate at which the investment was made is 9.4%.
2. Compound interest is calculated using the formula:
Compound Interest = Principal * (1 + Rate) ^ Time - Principal
In this case, the principal (P) is R12000, the final amount (A) is R15600, and the time (T) is 5 years. We need to determine the rate (R).
Let's substitute the values into the formula and solve for the rate (R):
Compound Interest = Principal * (1 + Rate) ^ Time - Principal
R15600 = R12000 * (1 + R) ^ 5 - R12000
To find the rate (R), rearrange the formula:
(1 + R) ^ 5 = (R15600 + R12000) / R12000
(1 + R) ^ 5 = 1.3
Taking the fifth root of both sides:
1 + R = (1.3)^(1/5)
1 + R ≈ 1.06
R ≈ 1.06 - 1
R ≈ 0.06
Therefore, the compound interest rate earned on the investment is approximately 6%.
To determine the simple interest rate at which an investment grew, we can use the formula:
Interest = Principal * Rate * Time
1. The value of an investment grew from R2200 to R3850 in 8 years. We know the Principal is R2200, and the final value is R3850. Time is given as 8 years. Let's calculate the rate:
Interest = R3850 - R2200 = R1650
Rate = Interest / (Principal * Time)
Rate = R1650 / (R2200 * 8)
Rate ≈ 0.094 / 8 ≈ 0.01175 or 1.175%
Therefore, the simple interest rate at which the investment was made is approximately 1.175%.
2. To determine the compound interest rate an investment earned, we can use the formula:
Final Amount = Principal * (1 + Rate) ^ Time
2. James had R12000 and invested it for 5 years. The final value is R15600. We need to find the compound interest rate:
Final Amount = R15600
Principal = R12000
Time = 5 years
Using the formula, we have:
R15600 = R12000 * (1 + Rate) ^ 5
To solve for the compound interest rate (Rate), we can rearrange the equation:
(1 + Rate) ^ 5 = R15600 / R12000
Now, take the fifth root of both sides to isolate the (1 + Rate):
1 + Rate = (R15600 / R12000)^(1/5)
Finally, subtract 1 from both sides to find the compound interest rate:
Rate = (R15600 / R12000)^(1/5) - 1
Calculate the expression (R15600 / R12000)^(1/5) and subtract 1 to find the compound interest rate.