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Financial Maths, STD2 2018 HSC 26c (Adapted)

Sofia contributes $175 to an annuity at the end of every month and plans to keep this up for 3 years.

Ignoring interest, how much will Sofia have paid into the annuity in total over the 3 years?   (1 mark)

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\(\text{Total contributed}=\$6300\)

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\(\text{Total contributed}=3\times 12\times 175=\$6300\)

Financial Maths, STD2 2013 23 MC (Adapted)

Elias opens a savings account that pays 4% per annum, compounded quarterly. At the end of every quarter he deposits $800, beginning one quarter after the account is opened, and continues for the following 18 months.

How much is in Elias’s account at the end of the 18 months?

  1. $4800.00
  2. $4921.61
  3. $4970.83
  4. $5095.30
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\(B\)

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\(\text{Interest: 4% p.a.}\ \ \Rightarrow\ \  \text{1% per quarter}\)

\(\text{18 months}=6\ \text{end-of-quarter deposits}\)

\(\text{Value of 1st deposit}=800(1.01)^5=840.81\)

\(\text{Value of 2nd deposit}=800(1.01)^4=832.48\)

\(\text{Value of 3rd deposit}=800(1.01)^3=824.24\)

\(\text{Value of 4th deposit}=800(1.01)^2=816.08\)

\(\text{Value of 5th deposit}=800(1.01)^1=808.00\)

\(\text{Value of 6th deposit}=800\)
   

\(\therefore\ \text{Amount in account}\)

\(=840.81+832.48+824.24+816.08+808.00+800.00\)

\(=\$4921.61\)

\(\Rightarrow B\)