Try a compound interest question.......

$43,252 is deposited into a bank account today at an interest rate of 2.05% p.a.

How much will be in the bank account in 10 year's time ? Round to TWO decimal places

Question

Try a compound interest question.......

$43,252 is deposited into a bank account today at an interest rate of 2.05% p.a.

How much will be in the bank account in 10 year's time ? Round to TWO decimal places

BlackTom AI · Accepted Answer

We start with the compound interest formula for a lump sum: A = P(1 + r)^t, where P is the present value, r is the annual interest rate, and t is the time in years.

Given values: P = 43,252, r = 0.0205 (which is 2.05%), t = 10 years.

Step 1: Substitute the values into the formula: A = 43,252 × (1 + 0.0205)^{10} = 43,252 × (1.0205)^{10}.

Step 2: Compute (1.0205)^{10}. A precise approach is to use successive multiplications or a calculator. A quick approximation uses natural logarithms: ln(1.0205) ≈ 0.020296, so 10 × ln(1.0205) ≈ 0.20296, and e^{0.20296} ≈ 1.2258. Therefore (1.0205)^{10} ≈ 1.2258. If you prefer a stepwise check: (1.0205)^2 ≈ 1.041..., (1.0205)^4 ≈ 1.084..., (1.0205)^8 ≈ 1.176..., and then multiply by (1.0205)^2 to reach (1.0205)^{10}, which aligns with the 1.22–1.23 range.

Step 3: Multiply the principal by the growth factor: 43,252 × 1.2258 ≈ 53,026.95.

Step 4: Round to two decimal places as requested: 53,026.95.

Summary: The account balance after 10 years is obtained by applying the compound growth factor (1.0205)^{10} to the initial deposit, yielding approximately 53,026.95 when rounded to two decimals.

BFIN011 Week 2: Practice Quiz

Try a compound interest question....... $43,252 is deposited into a bank account today at an interest rate of 2.05% p.a. How much will be in the bank account in 10 year's time ? Round to TWO decimal places

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