4.1H Compound Interest and Depreciation: Higher Tier Practice

EDEXCEL Edexcel 1MA1 · Calculator allowed · about 75 minutes

Total Marks

Name: _______________________________ Date: ____ / ____ / ______

Answer ALL questions. Show all your working.

Work out the value of £1200 after 2 years when it is invested at 3% compound interest, compounded annually.

(Total for Question 1 is 2 marks)

Zoe invests £800 at 4% compound interest, compounded annually, for 3 years. She then withdraws £200 from the account and the remaining amount earns 5% compound interest for one more year. Work out the amount in the account after these transactions. Give your answer to 2 decimal places.

(Total for Question 2 is 4 marks)

A delivery van depreciates in value by 12% each year. After 2 years its value is £788. Find its original value before depreciation. Give your answer to the nearest penny.

(Total for Question 3 is 3 marks)

Show that if an amount P is invested at an annual compound rate r (as a decimal) for n years, the value after n years is P(1 + r)ⁿ. You must give a clear algebraic argument.

(Total for Question 4 is 4 marks)

A laptop costs £500. It increases in value by 6% in year 1, by 3% in year 2, and then it depreciates by 5% in year 3. Work out its value after 3 years. Give your answer to 2 decimal places.

(Total for Question 5 is 5 marks)

An investment of £1500 grows to £1749.15 in 3 years with interest compounded annually. Work out the annual interest rate to 1 decimal place.

(Total for Question 6 is 4 marks)

Calculate the value of £2000 invested for 2 years at 3% per annum, compounded monthly. Give your answer to 2 decimal places.

(Total for Question 7 is 4 marks)

Priya invests £1500 at compound interest. After 4 years the amount is £1893.72.

a) Work out the annual compound interest rate. Give your answer as a percentage to 1 decimal place.

b) Priya withdraws £200 at the end of year 2. Work out how much she has in the account at the end of year 4. Give your answer to 2 decimal places.

c) At the end of year 4 she transfers the balance found in part (b) into a new account and immediately deposits an additional £500 into that new account. That new account earns 4% compound interest annually. Work out the total amount in the new account after 3 years. Give your answer to 2 decimal places.

(a)Work out the annual compound interest rate. Give your answer as a percentage to 1 decimal place.(3)

(b)Priya withdraws £200 at the end of year 2. Work out how much she has at the end of year 4. Give your answer to 2 decimal places.(6)

(c)At the end of year 4 she transfers the balance from part (b) into a new account and immediately deposits an extra £500. That new account pays 4% compound interest annually. Work out the total amount in the new account after 3 years. Give your answer to 2 decimal places.(5)

(Total for Question 8 is 14 marks)

Mark scheme · 4.1H Compound Interest and Depreciation: Higher Tier Practice

Question 1

M1 Use of compound growth: 1200 * (1 + 0.03)² or 1200 * 1.03²
A1 £1273.08 cao
Answer: 1273.08 (to 2 decimal places).

Question 2

M1 Amount after 3 years at 4%: 800 * 1.04³ or equivalent method
M1 Subtract 200 then apply 5%: (800*1.04³ - 200) * 1.05
A1 £734.89 awrt (intermediate correct values seen)
A1 £734.89 cao to 2 dp
Answer: 734.89

Question 3

M1 Set up: original * 0.88² = 788 or equivalent
M1 Divide: original = 788 / 0.88²
A1 £1017.56 cao
Answer: 1017.56

Question 4

dM1 Start: after 1 year amount = P(1 + r); after 2 years amount = P(1 + r)(1 + r) stated
dM1 Recognise repeated multiplication n times gives P(1 + r)ⁿ
A1 Conclude P(1 + r)ⁿ cao
C1 Clear communicative algebraic justification linking the repeated multiplication to exponent notation
Answer: P(1 + r)ⁿ, with algebraic justification as above.

Question 5

M1 Apply 6%: 500 * 1.06 or equivalent
M1 Then apply 3%: previous * 1.03
M1 Then apply depreciation 5%: previous * 0.95
A1 £518.61 awrt (intermediate correct)
A1 £518.61 cao to 2 dp
Answer: 518.61

Question 6

M1 Form ratio: (1749.15 / 1500) = (1 + r)³
M1 Take cube root: 1 + r = (1749.15 / 1500)^1/3
A1 Calculate r = (ratio)^1/3 - 1
A1 r = 5.3% to 1 dp cao
Answer: 5.3% (to 1 decimal place)

Question 7

M1 Use monthly rate 0.03/12 and n = 24: 2000*(1 + 0.03/12)²⁴
M1 Calculate (1 + 0.0025)²⁴ or equivalent
A1 £2123.51 awrt (intermediate correct shown)
A1 £2123.51 cao to 2 dp
Answer: 2123.51

Question 8

(a) M1 Form (1 + r)⁴ = 1893.72 / 1500
(a) M1 Take fourth root: 1 + r = (1893.72 / 1500)^1/4
(a) A1 r = 6.0% to 1 dp cao
(a) Answer: 6.0%
(b) M1 Calculate amount after 2 years: 1500 * 1.06²
(b) M1 Subtract 200 at end of year 2
(b) M1 Grow remaining amount for 2 more years: (amount after withdrawal) * 1.06²
(b) A1 £1669.00 awrt (intermediate seen)
(b) A1 £1669.00 cao to 2 dp
(b) C1 Clear multi-step working showing the sequence: grow, withdraw, grow
(b) Answer: 1669.00
(c) M1 Add extra deposit to balance from (b): 1669.00 + 500
(c) M1 Use 4% compound for 3 years: (sum) * 1.04³
(c) A1 Intermediate calculation shown correctly
(c) A1 £2439.83 awrt to 2 dp
(c) C1 Final answer stated with correct rounding and units
(c) Answer: 2439.83

Compound Interest and Depreciation: Higher Tier Practice - Worksheets, Questions and Revision