Jeremy invests RM 20,000 into an account that pays an interest rate of k % compounded quarterly. After five years, the account balance is RM 25,640.74. Determine the interest rate k% compounded quarterly
To find the interest rate, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the final account balance
P = the initial principal amount (RM 20,000 in this case)
r = the interest rate per compounding period
n = the number of times interest is compounded per year (4 in this case)
t = the number of years (5 in this case)
Plugging in the given values, we get:
25,640.74 = 20,000(1 + r/4)^(4*5)
Simplifying the equation, we have:
25,640.74 = 20,000(1 + r/4)^20
Dividing both sides by 20,000:
1.282037 = (1 + r/4)^20
Taking the 20th root of both sides:
(1 + r/4) = 1.282037^(1/20)
Now we can solve for r:
1 + r/4 = 1.013823
Subtracting 1 from both sides:
r/4 = 0.013823
Multiplying both sides by 4:
r = 0.055292
Converting to a percentage, the interest rate is approximately 5.53% compounded quarterly.