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Either paper 3 marks
Erin invests £4900 in a savings account.
The account pays simple interest at 2% per year.
Work out the total interest she earns after 6 years.
Show answer
\(\text{£}588\)Interest for one year:
\(4900 \times \frac{ 2 }{100} = 98\), so £98.
Simple interest pays the same amount every year, so after 6 years:
\(6 \times 98 = 588\)
Total interest = £588
- M1one year's interest \(£98\)
- M1multiplies by the number of years
- A1total interest \(£588\)
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Either paper 3 marks
Tomas puts £5400 into a savings account.
The account pays 3% simple interest per year.
(a)Find the interest paid in one year.
(b)Tomas takes nothing out of the account for 6 years.
Calculate how much is in the account at the end of the 6 years.
Show answer
(a) \(\text{£}162\)
(b) \(\text{£}6372\)\(5400 \times \frac{ 3 }{100} = 162\)
The interest for one year is £162.
Interest for 6 years: \(6 \times 162 = 972\)
Add it to the money paid in: \(5400 + 972 = 6372\)
There is £6372 in the account.
- (b) M1interest for 6 years \(972\)
- (b) A1balance \(6372\)
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Either paper 3 marks
Erin puts £6400 into a deposit account.
The account pays 5% simple interest per year.
She leaves the money in for 15 months.
Calculate the interest she earns.
Show answer
\(£400.00\)15 months is 1.25 years:
\(15 \div 12 = 1.25\) years
One whole year's interest would be:
\(6400 \times \dfrac{ 5 }{100} = £320\)
For 1.25 years:
\(£320 \times 1.25 = £400.00\)
- M1time as a fraction of a year \(1.25\)
- M1one whole year's interest \(£320\)
- A1interest \(£400.00\)
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Either paper 3 marks
Reuben invests £1000 for 7 years in an account that pays simple interest.
At the end of the 7 years he has earned £245 in interest.
Work out the annual rate of simple interest.
Show answer
\(3.5\%\)Interest for one year: \(245 \div 7 = 35\), so £35.
Write that as a percentage of the money invested:
\(\frac{ 35 }{ 1000 } \times 100 = 3.5\)
The rate is 3.5% per year.
- M1interest for one year \(35\)
- M1annual interest divided by the amount invested, \(\frac{ 35 }{ 1000 }\), times 100
- A1rate \(3.5\%\)
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Either paper 3 marks
Omar invests £1300 in an account paying 3% simple interest per year.
He leaves the money in the account until it has earned £195 in interest.
Calculate how many years the money is left in the account.
Show answer
\(5\ \text{years}\)Interest for one year:
\(1300 \times \frac{ 3 }{100} = 39\), so £39 each year.
Number of years:
\(195 \div 39 = 5\)
- M1one year's interest \(£39\)
- M1divides the total interest by one year's interest
- A1\(5\) years
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Either paper 5 marks
Nadia has \(£3000\) to invest.
Redwood Bank pays \(4\%\) simple interest per year. She would leave the money there for \(4\) years.
Halton Bank pays \(2\%\) simple interest per year. She would leave the money there for \(6\) years.
(a)Work out the interest she would earn at Redwood Bank.
(b)Work out the interest she would earn at Halton Bank.
(c)State which bank pays the more interest, and how much more.
Show answer
(a) \(£480.00\)
(b) \(£360.00\)
(c) Redwood Bank, by £120.00Simple interest pays the same amount every year, worked out on the original \(£3000\).
One year: \(4\%\) of \(£3000 = £120.00\)
\(4\) years: \(4 \times £120.00 = £480.00\)
One year: \(2\%\) of \(£3000 = £60.00\)
\(6\) years: \(6 \times £60.00 = £360.00\)
\(£480.00\) against \(£360.00\).
Redwood Bank pays \(£120.00\) more. The higher rate is not automatically the better account, because the two terms are different lengths.
- (a) M1one year of interest \(£120.00\)
- (a) A1interest \(£480.00\)
- (b) M1one year of interest \(£60.00\)
- (b) A1interest \(£360.00\)
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Either paper 4 marks
Zainab takes out a personal loan of £2900.
She is charged simple interest at 10% per year, for 2 years. The loan is repaid in equal instalments, one every month for the whole term.
Work out the fixed monthly repayment.
Show answer
\(£145.00\)Total interest over the whole term:
\(2900 \times \dfrac{ 10 }{100} \times 2 = £580\)
Total amount to repay:
\(£2900 + £580 = £3480\)
Number of monthly instalments over 2 years:
\(12 \times 2 = 24\)
Monthly repayment:
\(£3480 \div 24 = £145.00\)
- M1total interest \(£580\)
- M1total to repay \(£3480\)
- M1number of instalments \(24\)
- A1monthly repayment \(£145.00\)
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Either paper 3 marks
Tomas invests some money in a fixed-rate bond that pays 6% simple interest per year.
After 2 years the bond matures. In total he receives £15008 — the original amount invested, plus all the interest earned.
Find the amount he originally invested.
Show answer
\(\text{£}13400\)Each year the bond adds 6% of the original amount, so after 2 years the payout is:
\(100 + (6 \times 2) = 112\%\) of the original amount.
Divide the total by this multiplier:
\(£15008 \div \dfrac{ 112 }{100} = £15008 \times \dfrac{100}{ 112 } = £13400\)
The amount originally invested was £13400.
- M1multiplier \(112\%\)
- M1divides the total by the multiplier
- A1original amount \(£13400\)
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Either paper 3 marks
Isla puts money into an investment. It pays a fixed rate of simple interest every year, and she leaves the money in for 2 years.
Over that time, the total interest she earns is \(\dfrac{ 1 }{ 10 }\) of the amount she originally invested.
Calculate the annual rate of simple interest.
Show answer
\(5\ \%\)No principal is given, so eliminate it — either cancel it from the formula, or simply choose a convenient value for it, such as £100.
Taking the principal as £100:
\(\dfrac{ 1 }{ 10 } \times £100 = £10\)
Using \(I = \dfrac{PRT}{100}\) with \(P = 100\):
\(10 = R \times 2\)
\(R = \dfrac{ 10 }{ 2 } = 5\)
The annual rate of simple interest is 5%.
- P1interest \(10\) on a principal of 100
- M1equation \(10 = R \times 2\)
- A1rate \(5\)%
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Either paper 5 marks
Sofia and Deniz share an inheritance of £10000 in the ratio \(4 : 1\) (Sofia to Deniz).
Each of them puts their own share into a savings account that pays 2% simple interest per year.
(a)Work out how much of the £10000 Sofia and Deniz each receive.
(b)Sofia and Deniz both leave their money in the account for 3 years.
Work out how much more interest Sofia earns than Deniz.
Show answer
(a) Sofia: £8000, Deniz: £2000
(b) \(\text{£}360\)Total number of parts: \(4 + 1 = 5\)
One part: \(£10000 \div 5 = £2000\)
Sofia: \(4 \times £2000 = £8000\)
Deniz: \(1 \times £2000 = £2000\)
Sofia's interest: \(£8000 \times \dfrac{ 2 }{100} \times 3 = £480\)
Deniz's interest: \(£2000 \times \dfrac{ 2 }{100} \times 3 = £120\)
Difference: \(£480 - £120 = £360\)
- (a) M1one part \(2000\) pounds, from the total divided by \(5\) parts
- (a) A1shares £8000 and £2000
- (b) M1interest on one share \(£480\)
- (b) M1interest on the other share \(£120\)
- (b) A1difference £360