Grade 10 Maths · Financial Maths · Find the interest rate or time

Find the interest rate or time Grade 10

Work backwards from P and A to find the interest rate (simple, or compound using a root) or the number of years for simple interest, for example R1 000 growing to R1 210 in 2 years gives 1 + i = 1,21, so i = 10\%.

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Financial Maths Grade 10 | Compound Interest ( Finding Interest rates Explained )Gridwell Maths Tutoring

Financial Maths Grade 10 | Simple interest ( Finding interest rate Explained )Gridwell Maths Tutoring

Financial Maths Grade 10 | Simple interest ( Finding Number of Years Explained )Gridwell Maths Tutoring

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Question 6.1 · November 2022 · Paper 1 · National (DBE) · 4 marks

6.1 R12 000 was invested in a fund that paid interest at

m %

p.a., compounded quarterly. After 24 months, the value of the investment was R13 459.

Determine the value of

m

.(4)

Work it out on paper first. Then mark yourself with the official memo, one tick at a time.

More questions: find the interest rate or time

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3. Question 6.1.1 · November 2023 · Paper 1 · National (DBE) · 3 marks
6.1 Patrick deposited an amount of R18 500 into an account earning $r %$ interest p.a., compounded monthly. After 6 months, his balance was R19 319,48.

Answer the questions that follow.
6.1.1 Calculate the value of $r$ .(3)
Show the memo (3 ticks)Memo
1. ✓
  $n = 6$ $n = 6$
  1 mark · Find i and n per period
2. ✓
  Substitution into correct formula $A = P (1 + i)^{n}$
  $19319, 48 = 18500 (1 + \frac{r}{1200})^{6}$
  1 mark · Find the interest rate or time
3. ✓
  Answer $(1 + \frac{r}{1200}) = 6 1, 04429 \dots$
  $\frac{r}{1200} = 0, 00725 \dots$
  $r = 8, 7%$
  1 mark · Find the interest rate or time
4. Practice · Siyavula Grade 10 Maths · Ex 9.2 · 3 marks
Kabir invests R1 790 into an account which pays out a lump sum at the end of $9$ years. If he gets R2 613,40 at the end of the period, what compound interest rate did the bank offer him? Give the answer correct to one decimal place.(3)
Show the memo (3 ticks)Memo
1. ✓
  Substitution $A = P (1 + i)^{n}$
  $2613, 40 = 1790 (1 + i)^{9}$
  1 mark · Find the interest rate or time
2. ✓
  Isolate the bracket and take the root $(1 + i)^{9} = \frac{2 613 , 40}{1 790} = 1, 46$
  $1 + i = 9 1, 46$
  1 mark · Find the interest rate or time
3. ✓
  Answer as a percentage $i = 0, 0429$ , so the rate is $4, 3%$ p.a.
  1 mark · Find the interest rate or time
Question adapted from Siyavula Education (CC BY 3.0) · Solution by NavyBlue
5. Practice · Siyavula Grade 10 Maths · Ex 9.1 · 2 marks
Abdoul wants to invest R1 080 at a simple interest rate of $10, 9%$ p.a. How many years will it take for the money to grow to R3 348? Round up your answer to the nearest year.(2)
Show the memo (2 ticks)Memo
1. ✓
  Substitution $3348 = 1080 (1 + 0, 109 n)$
  1 mark · Find the interest rate or time
2. ✓
  Answer $3, 1 = 1 + 0, 109 n$
  $n = \frac{2 , 1}{0 , 109} = 19, 27$
  It takes $20$ years.
  1 mark · Find the interest rate or time
Question adapted from Siyavula Education (CC BY 3.0) · Solution by NavyBlue
6. Practice · Siyavula Grade 10 Maths · Ex 9.2 · 3 marks
Bongani invests R6 110 into an account which pays out a lump sum at the end of $7$ years. If he gets R6 904,30 at the end of the period, what compound interest rate did the bank offer him? Give the answer correct to one decimal place.(3)
Show the memo (3 ticks)Memo
1. ✓
  Substitution $A = P (1 + i)^{n}$
  $6904, 30 = 6110 (1 + i)^{7}$
  1 mark · Find the interest rate or time
2. ✓
  Isolate the bracket and take the root $(1 + i)^{7} = \frac{6 904 , 30}{6 110} = 1, 13$
  $1 + i = 7 1, 13$
  1 mark · Find the interest rate or time
3. ✓
  Answer as a percentage $i = 0, 0176$ , so the rate is $1, 8%$ p.a.
  1 mark · Find the interest rate or time
Question adapted from Siyavula Education (CC BY 3.0) · Solution by NavyBlue

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