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Chris opens a bank account and deposits $1000 into it - HSC - SSCE Mathematics Standard - Question 3 - 2019 - Paper 1

Question 3

Chris opens a bank account and deposits $1000 into it. Interest is paid at 3.5% per annum, compounding annually. Assuming no further deposits or withdrawals are mad... show full transcript

Worked Solution & Example Answer:Chris opens a bank account and deposits $1000 into it - HSC - SSCE Mathematics Standard - Question 3 - 2019 - Paper 1

Step 1

Calculate the balance after 1 year

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Answer

To find the balance after the first year, use the formula for compound interest: $A = P(1 + r)^t$ where:

$A$ is the amount of money accumulated after n years, including interest.
$P$ is the principal amount (the initial deposit).
$r$ is the annual interest rate (decimal).
$t$ is the time the money is invested for in years.

Substituting the values:

$P = 1000$
$r = 0.035$
$t = 1$

Calculating: $A = 1000(1 + 0.035)^1 = 1000 imes 1.035 = 1035$

Step 2

Calculate the balance after 2 years

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Answer

Using the same formula for the second year: $A = P(1 + r)^t$ Here, the principal amount is now $1035 (the amount from year 1).

So, for the second year, substituting the values:

$P = 1035$
$r = 0.035$
$t = 1$

Calculating: $A = 1035(1 + 0.035)^1 = 1035 imes 1.035 = 1071.225$

Rounding to the nearest cent gives us $1071.23.

Step 3

Conclusion of options

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Answer

Therefore, the balance in the account at the end of two years will be $1071.23, which corresponds to option B.

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