An investment of 5,000 USD is placed into an account earning 6% annual interest compounded semi-annually. What is the total account balance at the end of 2 years?
Answer and explanation
Correct answer: D. 5,627.54 USD
- Step 1: Compound interest formula: A = P(1 + r/n)^(nt).
- Step 2: Here, P = 5,000 USD, annual rate r = 0.06, compounding frequency n = 2 (semi-annually), time t = 2 years.
- Step 3: n t = 2 2 = 4 compounding periods.
- Step 4: Periodic interest rate r/n = 0.06 / 2 = 0.03.
- Step 5: A = 5000 (1 + 0.03)^4 = 5000 (1.03)^4.
- Step 6: (1.03)^2 = 1.0609.
- Step 7: (1.03)^4 = (1.0609)^2 = 1.12550881.
- Step 8: A = 5000 * 1.12550881 = 5,627.54 USD.
Answer
5,627.54 USD.
Why not the others: '5,600.00 USD' is simple interest (5000 0.06 2 = 600); '5,618.00 USD' compounds annually (n=1); '5,650.00 USD' is an overestimation.
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