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Financial Maths - Series - Annuities - Finding n and changing terms.
Test Yourself 1 - Solutions.


 

Finding n for a
pre-determined total.		 1. r = 4.8%÷12 = 0.004.

(i) Compound interest as only 1 deposit.

Value = $300 × 1.0045 = $306.05

 

(ii) End of month 1 = M1 = 300 × 1.004

End M2 = (300 × 1.04 + 300) × 1.004

End M3 =
((300 × 1.04 + 300) × 1.004 + 300) × 1.004

= 1.004 × 300 × (1 + 1.004 + 1.0042)

(NOTE: 3 months and 3 terms in brackets)

So end Mn = 1.004 × 300 × .

∴ 20000 = 1.004 × 300 × .

1 - 1.004n = -0.2656

1.004n = 1.2656

n = 59 months.
  2.
  3.
Missing payments. 4. (i)

(ii) For the two years Amy is on leave when no further payments are being made, the amount in the fund receives only compound interest.

(iii)

(iv)

So the maternity leave taken by Amy has cost her
$410,735.23 - $346,323.33 = $64,411.90.

For all the figures we are computing in these exercises, we must think of the broader implications because the results are not just numbers. Consider what some of the social and economic implications of this reduction might be - to Amy and her family as well as to the broader community and society.
  5. (i)

(ii)

(iii)

(iv)

(v) $223542.59 - $176,052.37 = $47,490.22.
Increasing interest rate or deposit. 7. 6% p.a. = 0.5% p.m. Let $A be Ben's monthly contribution.

(i) End M1 = A × 1.005

End M2 = [(A× 1.005) + A]1.005 = A×1.0052 + A×1.005

End M3 = [A×1.0052 + A×1.005 + A]1.005

= A×1.005 (1 + 1.005 + 1.0052)

(ii) To reach $8000,

(iii) At the end of 24 months at $203 per month, Ben has saved

So for the final 12 months, Ben contributes $203 but
at 9% = 0.0075 which adds to the $5,188.50
compounded for the 12 months.

So an extra $233 dollars.
  8. (i)

(ii)