Final answer:
The compound interest rate is found using the formula FV = P * (1 + r)^t, where P is principal, r is rate, t is time, and FV is future value. After calculating with the given values, an interest rate of approximately 0.87% is found, which does not match any of the provided options. There may be a typo or an error in the question or options listed.
Step-by-step explanation:
To calculate the compound interest rate per annum, we use the formula for compound interest, which states that the future value (FV) is equal to the principal amount (P) multiplied by one plus the annual interest rate (r), raised to the power of the number of years (t).
The formula is:
FV = P * (1 + r)^t
Given:
- Principal (P) = GH¢45,600.00
- Interest earned = GH¢1,200.00
- Time period (t) = 3 years
We aim to find the rate (r). To do so, we first calculate the total amount accumulated after 3 years, which is the principal plus the interest earned:
Total amount = Principal + Interest earned = GH¢45,600.00 + GH¢1,200.00 = GH¢46,800.00
Now we plug these values into the formula and solve for r:
GH¢46,800.00 = GH¢45,600.00 * (1 + r)^3
Next, divide both sides by GH¢45,600.00:
(1 + r)^3 = GH¢46,800.00 / GH¢45,600.00 = 1.026315789
Now take the cube root of both sides to find (1 + r):
1 + r = (1.026315789)^(1/3)
After calculating the cube root:
1 + r = 1.008666577
Subtract 1 from both sides to solve for r:
r = 1.008666577 - 1 = 0.008666577
Convert this to a percentage:
r = 0.008666577 * 100% = 0.8666577%