JeremyinvestsRM20,000intoanaccountthatpaysaninterestrateofk%compounded quarterly. After 􏰀ive years, the account balance is RM 25,640.74. Determine the interest rate k % compounded quarterly.

Answer 1

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%.