A shopkeeper Invested sh 4800000 for 5 years .if the amount of money calculated is sh 7730450 calculate the compound interest rate?

To calculate the compound interest rate, we can use the formula:

A = P(1 + r/n)^(nt)

Where:
A = the amount of money after t years (sh 7730450)
P = the principal amount (sh 4800000)
r = the annual interest rate
n = the number of times interest is compounded per year (assuming it is compounded annually)
t = the number of years (5 years)

Substitute the given values into the formula:

7730450 = 4800000(1 + r/1)^(1*5)

7730450 = 4800000(1 + r)^5

7730450 / 4800000 = (1 + r)^5

1.61009375 = (1 + r)^5

Taking the fifth root of both sides:

(1 + r) = 1.210

r = 0.210 or 21%

Therefore, the compound interest rate is 21%.

Step 1: Find the interest earned

Interest = Amount - Principal
Interest = 7730450 - 4800000
Interest = 2930450

Step 2: Calculate the interest rate per year

Interest rate per year = (Interest / Principal) - (1 / Number of years)
Interest rate per year = (2930450 / 4800000) - (1 / 5)
Interest rate per year = 0.121

Step 3: Convert to a compound interest rate

r = [(1 + i)^n - 1] - 100
Where:
- r is the compound interest rate
- i is the interest rate per year
- n is the number of years

r = [(1 + 0.121)^5 - 1] - 100
r = 14.49%

Therefore, the compound interest rate is 14.49%.