Unit 4
6 marks · Normal1. Rajiv invests £2500 at 4% compound interest per annum. After 3 years, he decides to use the total amount to build a rectangular flowerbed. The width of the flowerbed is 1.5 m and its length is twice the width.
Calculate the value of Rajiv's investment after 3 years. Give your answer to the nearest pound.
He decides to spend the entire amount on fencing the four sides of the flowerbed. The fencing costs £50 per metre. Work out the length of fencing Rajiv can buy, and state whether this is more or less than the perimeter of his planned flowerbed.
Find the area of the flowerbed in square metres.
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) £2813 pounds
(b) He can buy 56.26 m; the perimeter of the planned bed is 9 m. He can buy much more fencing than needed.
(c) 4.5 m^2
Show mark scheme and worked solution
Marking points
M1 (a) · 1 mark · Uses the correct formula for compound interest.
A1 (a) · 1 mark · Correctly calculates final amount (£2813 to nearest pound). (follow-through)
M2 (b) · 1 mark · Finds perimeter of flowerbed correctly (1.5 m × 2 + 3 m × 2 = 9 m) and calculates total possible fencing length (Total money / 50). (follow-through)
A2 (b) · 1 mark · Draws correct conclusion about comparison (fencing is more than required). (follow-through)
M3 (c) · 1 mark · Finds area: width × length = 1.5 m × 3 m.
A3 (c) · 1 mark · Correct area given as 4.5 m^2 (with tolerance).
Worked solution
a) Use compound interest formula: Total = £2500 × (1.04)^3 = £2500 × 1.124864 = £2812.16 ≈ £2813.
b) Perimeter of flowerbed = 2 × (1.5 + 3) = 9 m. Fencing: £2813 / £50 = 56.26 m. So, Rajiv can buy much more fencing than required.
c) Area = width × length = 1.5 m × 3 m = 4.5 m^2.