Define simple interest .

Simple interest is interest calculated only on the starting amount , so every interest payment is exactly the same size. The total is found by taking the percentage of the starting amount once, then multiplying by the number of time periods.

Define compound interest .

Compound interest is interest calculated on the running total , so each payment is worked out on a balance that already includes the earlier interest. That makes every payment slightly larger than the one before it.

When you work out compound interest using a multiplier, does the result give the interest earned or the total balance?

The calculation gives the total balance at the end of the period, not the interest earned. To find just the interest, subtract the original amount from that final balance.

Why is AER used when comparing savings accounts?

Savings accounts pay interest at different rates and at different intervals, so their headline rates cannot be compared directly. AER folds both of those into a single annual figure , so the best return is simply the account with the highest AER.

What is the key difference between savings and investments?

The key difference is the level of risk : savings earn a known, guaranteed rate of interest, while the value of an investment can go down as well as up. Investments offer potentially higher returns in exchange for the risk that money may be lost.

Give one advantage and one disadvantage of investing rather than saving.

The advantage is the chance of higher returns , with a choice of risk levels available. The disadvantages are that money may be lost overall, that the value fluctuates up and down, and that funds may take longer to withdraw.

Bank A pays 7.16% annually with interest paid monthly, B pays 7.15% paid weekly, and C pays 7.17% paid quarterly. Which gives the best return?

Bank B , at an AER of 7.407%, even though its headline rate is the lowest of the three. Paying interest weekly compounds it 52 times a year, which more than makes up for the slightly lower nominal rate.

Why does a borrower always pay back more than they borrowed?

Interest is charged at regular intervals and added on to the amount owed. The interest is the fee the borrower pays the lender for the service of providing a large sum of money straight away.

Define a secured loan.

A secured loan is one that is tied to an asset, such as a mortgage secured against the property being bought. If the borrower does not keep up the payments, the lender has the right to take back that asset.

Why is a mortgage paid off most slowly at the start of its term?

At the start the balance owed is at its largest, so most of each monthly payment is swallowed by the interest charged on it. As the balance falls the interest added each month falls too, so a growing share of the same fixed payment goes into clearing the debt.

True or False? Every student loan is eventually paid off in full.

False. Because repayments depend on income and interest keeps being added to the balance, many borrowers never repay the whole amount. Each plan has a point at which the remaining balance is written off , so any debt still outstanding at that stage is cancelled.

Why is APR useful when comparing loans?

Different loans have different terms, fees and repayment schedules, which makes them impossible to compare directly. APR folds the amount borrowed, the interest and the timing of every repayment into a single figure , and UK lenders are legally required to disclose it.

Define LTV , the loan to value ratio.

LTV is the amount borrowed written as a proportion of the value of the property, usually expressed as a percentage. A larger deposit gives a lower LTV, which often earns the borrower a lower interest rate.

Payday loans and mortgages are both forms of borrowing. What is the main difference in the way they cost money?

Payday loans are short-term and carry extremely high interest rates, while mortgages carry relatively low ones. A mortgage still costs a great deal in total, though, because the amount borrowed is large and the term runs for decades.

Define equity in a property.

Equity is the share of the property that the borrower actually owns. A 10% cash deposit gives 10% equity at the start, and the equity reaches 100% once the mortgage has been fully repaid.

Name two ways a student loan differs from a loan taken out with a bank.

For an employee, student loan repayments are taken straight out of their salary , at the same time as income tax and National Insurance. Student loans are also provided or backed by the government rather than by a private lender.

£5000 is borrowed and repaid with two annual payments of £3000. Why is the true interest rate not simply 10%?

The £1000 of interest is not spread evenly over the two years, because the first £3000 payment reduces the balance before the second year's interest is charged. Working the rate out properly gives an APR of about 13.07% , which is exactly why lenders must quote APR rather than a simple average.

Under a hire purchase agreement, when does the buyer actually own the item?

Ownership passes only once the full amount has been paid off. Until then the item, commonly a car, still belongs to the lender even though the buyer is the one using it.

What happens to a mortgage's interest rate when its fixed term ends?

The rate switches to a variable one linked to the Bank of England base rate, so the monthly payment can then rise or fall. The alternative is to agree another fixed term, which is called remortgaging .

What determines how much a lender will offer someone for a mortgage?

Lenders test affordability , which depends on the borrower's income, expenses, existing debts and credit history. Most will lend around 4.5 times annual salary as a rough guide, though each lender sets its own criteria and accepts a different level of risk.

Level 3MathsAQAMathematical Studies (Core Maths)Paper 1: Data, Finance, Estimation & ModellingFlashcardsPersonal FinanceSaving & Borrowing

Saving & Borrowing (AQA Level 3 Mathematical Studies (Core Maths): Paper 1: Data, Finance, Estimation & Modelling): Flashcards

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Define simple interest.

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Cards in this collection (28)

Define simple interest.
Simple interest is interest calculated only on the starting amount, so every interest payment is exactly the same size.
The total is found by taking the percentage of the starting amount once, then multiplying by the number of time periods.
Define compound interest.
Compound interest is interest calculated on the running total, so each payment is worked out on a balance that already includes the earlier interest.
That makes every payment slightly larger than the one before it.
When you work out compound interest using a multiplier, does the result give the interest earned or the total balance?
The calculation gives the total balance at the end of the period, not the interest earned.
To find just the interest, subtract the original amount from that final balance.
An amount $P$ grows at an annual interest rate $r$ , written as a decimal. Complete the formula for the balance after $n$ years, including the missing index.
$balance = P {(______+ r)}^{______}$
The completed formula is:
$balance = P {(1 + r)}^{n}$
The multiplier $1 + r$ is applied once for each period, which is why it is raised to the power $n$ .
Why is AER used when comparing savings accounts?
Savings accounts pay interest at different rates and at different intervals, so their headline rates cannot be compared directly.
AER folds both of those into a single annual figure, so the best return is simply the account with the highest AER.
A bank pays 4% simple interest. £250 is left in the account for 6 years. How much interest is earned?
Find 4% of the starting amount once, giving $0.04 \times 250 = 10$ , then multiply by the number of years.
That gives $10 \times 6 = 60$ , so £60 of interest is earned and the balance ends at £310.
True or False?
For a savings account that pays interest once a year, the AER equals the nominal interest rate.
True.
With one compounding period a year the formula gives ${(1 + i)}^{1} - 1 = i$ , so there is no compounding within the year to make any difference.
AER only differs from the nominal rate when interest is paid more than once a year.
£4000 is invested at 5% compound interest per year. How do you find how many years it takes to reach £6000?
Write $4000 \times 1 . 05^{n} = 6000$ and find $n$ by trial and error, testing whole numbers of years.
Since $4000 \times 1 . 05^{8} = 5909.82$ and $4000 \times 1 . 05^{9} = 6205.31$ , the balance first passes £6000 after 9 years.
What is the key difference between savings and investments?
The key difference is the level of risk: savings earn a known, guaranteed rate of interest, while the value of an investment can go down as well as up.
Investments offer potentially higher returns in exchange for the risk that money may be lost.
In the AER formula, what do $i$ and $n$ stand for, and what form must $i$ take?
In that formula $i$ is the nominal interest rate per annum, and $n$ is the number of compounding periods in a year.
Both $i$ and the answer $r$ must be written as decimals, so a rate quoted per month has to be multiplied by 12 before it is used.
Give one advantage and one disadvantage of investing rather than saving.
The advantage is the chance of higher returns, with a choice of risk levels available.
The disadvantages are that money may be lost overall, that the value fluctuates up and down, and that funds may take longer to withdraw.
Bank A pays 7.16% annually with interest paid monthly, B pays 7.15% paid weekly, and C pays 7.17% paid quarterly. Which gives the best return?
Bank B, at an AER of 7.407%, even though its headline rate is the lowest of the three.
Paying interest weekly compounds it 52 times a year, which more than makes up for the slightly lower nominal rate.
£9000 earns simple interest for 5 years and grows to £11 700. How do you find the rate?
Find the total interest of £2700, then divide by 5 to get the £540 earned each year.
Express that as a percentage of the original £9000, giving $540 \div 9000 = 0.06$ , so the rate is 6%.
Why does a borrower always pay back more than they borrowed?
Interest is charged at regular intervals and added on to the amount owed.
The interest is the fee the borrower pays the lender for the service of providing a large sum of money straight away.
Define a secured loan.
A secured loan is one that is tied to an asset, such as a mortgage secured against the property being bought.
If the borrower does not keep up the payments, the lender has the right to take back that asset.
Complete the rule for a monthly student loan repayment.
The repayment is a fixed $______$ of the amount earned above a $______$ each month.
The completed rule is:
The repayment is a fixed percentage of the amount earned above a threshold each month.
Someone earning £3000 a month against a £2083 threshold pays that percentage on the £917 difference only, not on the whole £3000.
Why is a mortgage paid off most slowly at the start of its term?
At the start the balance owed is at its largest, so most of each monthly payment is swallowed by the interest charged on it.
As the balance falls the interest added each month falls too, so a growing share of the same fixed payment goes into clearing the debt.
True or False?
Every student loan is eventually paid off in full.
False.
Because repayments depend on income and interest keeps being added to the balance, many borrowers never repay the whole amount.
Each plan has a point at which the remaining balance is written off, so any debt still outstanding at that stage is cancelled.
Why is APR useful when comparing loans?
Different loans have different terms, fees and repayment schedules, which makes them impossible to compare directly.
APR folds the amount borrowed, the interest and the timing of every repayment into a single figure, and UK lenders are legally required to disclose it.
Define LTV, the loan to value ratio.
LTV is the amount borrowed written as a proportion of the value of the property, usually expressed as a percentage.
A larger deposit gives a lower LTV, which often earns the borrower a lower interest rate.
Payday loans and mortgages are both forms of borrowing. What is the main difference in the way they cost money?
Payday loans are short-term and carry extremely high interest rates, while mortgages carry relatively low ones.
A mortgage still costs a great deal in total, though, because the amount borrowed is large and the term runs for decades.
In the APR formula, what do $A_{k}$ and $t_{k}$ stand for?
In that formula $A_{k}$ is the amount of the $k$ th repayment, and $t_{k}$ is the interval in years between the start of the loan and that repayment.
The rate $i$ has to be entered as a decimal, and the formula assumes there are no arrangement or exit fees.
Define equity in a property.
Equity is the share of the property that the borrower actually owns.
A 10% cash deposit gives 10% equity at the start, and the equity reaches 100% once the mortgage has been fully repaid.
Name two ways a student loan differs from a loan taken out with a bank.
For an employee, student loan repayments are taken straight out of their salary, at the same time as income tax and National Insurance.
Student loans are also provided or backed by the government rather than by a private lender.
£5000 is borrowed and repaid with two annual payments of £3000. Why is the true interest rate not simply 10%?
The £1000 of interest is not spread evenly over the two years, because the first £3000 payment reduces the balance before the second year's interest is charged.
Working the rate out properly gives an APR of about 13.07%, which is exactly why lenders must quote APR rather than a simple average.
Under a hire purchase agreement, when does the buyer actually own the item?
Ownership passes only once the full amount has been paid off.
Until then the item, commonly a car, still belongs to the lender even though the buyer is the one using it.
What happens to a mortgage's interest rate when its fixed term ends?
The rate switches to a variable one linked to the Bank of England base rate, so the monthly payment can then rise or fall.
The alternative is to agree another fixed term, which is called remortgaging.
What determines how much a lender will offer someone for a mortgage?
Lenders test affordability, which depends on the borrower's income, expenses, existing debts and credit history.
Most will lend around 4.5 times annual salary as a rough guide, though each lender sets its own criteria and accepts a different level of risk.

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