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Higher Applications of Maths finance: effective rates, present values and loans

Finance carries the largest share of the question paper. It rests on one idea: money now and money later are compared by moving them to the same date with an effective rate of interest.

Rates	Effective rates, fixed or varying, over different time periods
Values	Present and accumulated values of single payments and series
Products	Loans, credit cards, savings, pensions and insurance
Planning	Tax, inflation, purchasing power and risk

Match the rate to the period

A monthly payment needs a monthly effective rate. Convert first: an annual effective rate of 6% gives a monthly rate of 1.06 to the power one twelfth, minus 1, about 0.487%; a monthly rate of 1% gives an annual rate of 1.01 to the power 12, minus 1, about 12.68%.

Move every payment to one date

To compare two plans, discount or accumulate every payment to the same date, then compare the totals. A deferred series is valued at the start of the payments, then discounted for the deferral.

Use the figures the question gives

Tax bands, allowances and interest rates change, so questions give the ones to use. Read them from the question or its data, and keep every amount to the penny.

Try 2 questions

Question 1Calculator or spreadsheet

Three savings accounts. Account A: effective rate 4.2% per year. Account B: effective rate 0.35% per month. Account C: effective rate 2.1% per half year.
Account	Effective rate of interest
A	4.2% per year
B	0.35% per month
C	2.1% per half year

Three savings accounts pay interest as shown in the table. Given that

1.0035^{12}

= 1.042818

and

1.021^{2}

= 1.042441

, which account has the highest effective annual rate of interest?

Question 2Calculator or spreadsheet

Credit card spreadsheet. Month 1: opening balance 2400.00, interest 38.40, payment 150.00, closing balance 2288.40. Month 2: opening 2288.40, interest 36.61, payment 150.00, closing 2175.01. Month 3: opening 2175.01, interest 34.80, payment 150.00, closing 2059.81. All amounts in pounds.
Month	Opening balance (pounds)	Interest (pounds)	Payment (pounds)	Closing balance (pounds)
1	2400.00	38.40	150.00	2288.40
2	2288.40	36.61	150.00	2175.01
3	2175.01	34.80	150.00	2059.81

Nina owes 2400 pounds on a credit card. Each month, interest of 1.6% of the opening balance is added, rounded to the nearest penny, and then she pays 150 pounds. She makes no new purchases. The spreadsheet shows the first three months. What is her closing balance for month 4?

Next step

Take the free test Start the effective rates lesson

Questions people ask

Do I need to learn the current tax rates?

No. Questions give the rates, bands and allowances to use.

Do I need a spreadsheet for finance questions?

In the exam you have spreadsheet software, and long schedules of payments are easiest built in it. Here, the questions show the rows or give the values so that you practise the method and the decision.