JeremyinvestsRM20,000intoanaccountthatpaysaninterestrateofk%compounded quarterly. After ive years, the account balance is RM 25,640.74. Determine the interest rate k % compounded quarterly.
To determine the interest rate, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
where A is the final account balance, P is the principal amount, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years.
In this case, P = RM20,000, A = RM25,640.74, n = 4 (compounded quarterly), and t = 5 years. We want to find the value of r.
25,640.74 = 20,000(1 + r/4)^(4*5)
Dividing both sides by 20,000:
1.282037 = (1 + r/4)^20
Taking the 20th root of both sides:
(1.282037)^(1/20) = 1 + r/4
Subtracting 1 from both sides:
(1.282037)^(1/20) - 1 = r/4
Multiplying both sides by 4:
4 * [(1.282037)^(1/20) - 1] = r
Using a calculator:
r ≈ 0.03475
Multiplying by 100 to get the interest rate in percentage:
k ≈ 3.475%
Therefore, the interest rate k compounded quarterly is approximately 3.475%.