Unit 4
5 marks · NormalA saving scheme gives interest at 4% per year, compounded annually. The sequence of balances over five years is plotted on a graph. Simultaneously, an algebraic expression relates to the yearly deposit amount.
Amira deposits $3000. Calculate the total value of her savings after 5 years.
The graph of Amira's savings, plotted against number of years n, is shown below.
Describe how the graph shows that the total increases by a larger amount each year.
Write an algebraic expression for the value S after n years using the starting amount $3000 and the yearly multiplying factor.
Work this out on paper, then compare with the answer and worked solution below. With a free account you can submit written answers for marking.
Show answer
(a) $3650 dollars
(b) The curve becomes steeper, showing yearly increases get bigger.
(c) S = 3000 × 1.04ⁿ
Common mistakes: linear instead of compound calculation; incorrect algebraic notation
Show mark scheme and worked solution
Marking points
M1 (a) · 1 mark · Uses S = 3000 × (1.04)^5 or step-by-step correct calculation
A1 (a) · 1 mark · Gives value to at least nearest dollar: $3650 (follow-through)
B1 (b) · 1 mark · Recognises graph is a curve, not a straight line, with increasing increment
M2 (c) · 1 mark · States correct form S = 3000 × (1.04)^n or equivalent
A2 (c) · 1 mark · Uses index notation and both correct numbers (starting amount, multiplier) (follow-through)
Worked solution
a) S = 3000 × (1.04)^5 ≈ 3000 × 1.2166529 ≈ $3649.96 ≈ $3650
b) The graph curves upward, showing the increase each year is greater than the year before.
c) S = 3000 × (1.04)^n