Final answer:
The simple interest on $2,000 at a rate of 2% for 3 years is $120. When compounded annually the interest is $122.42, when compounded semi-annually it's $123.61, and when compounded quarterly it's $124.62.
Step-by-step explanation:
Calculating Interest Earned
To analyze how the principal amount of $2,000 earns interest in different scenarios over three years with an interest rate of 2%, we'll use both the simple interest formula and the compound interest formula.
a. Simple Interest
Using the simple interest formula I = PRT, where I is interest, P is principal, R is the interest rate, and T is time in years:
I = $2,000 × 0.02 × 3 = $120
The simple interest earned over three years is $120.
b. Compound Interest (Annually)
Using the compound interest formula A = P(1 + r/n)^(nt), where A is the 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:
A = $2,000 × (1 + 0.02/1)^(1×3) = $2,000 × 1.02^3 = $2,000 × 1.061208 ≈ $2,122.42
The interest compounded annually is $122.42.
c. Compound Interest (Semi-annually)
A = $2,000 × (1 + 0.02/2)^(2×3) = $2,000 × 1.01^6 ≈ $2,123.61
The interest compounded semi-annually is $123.61.
d. Compound Interest (Quarterly)
A = $2,000 × (1 + 0.02/4)^(4×3) = $2,000 × 1.005^12 ≈ $2,124.62
The interest compounded quarterly is $124.62.