Transcript Angles - Nuffield Foundation

Useful Savings Facts & Formulae
The amount invested is called the principal
When a principal £P earns compound interest at an
annual rate R for n years, the final amount is:
A = P (1 + R)n
The annual rate at which a principal £P would increase to
an amount £P in n years is:
A
R=
AER =
n
P
–1
Interest earned in 1 year
 100%
Amount at the beginning of the year
The AER corresponding to rate r added n times per year is:
R = (1 + r)n – 1
Example
A = P (1 + R)n
Neil invests £2000 at 4.2% per annum.
Calculate the amount after 10 years.
R=
4.2
100 = 0.042
A = 2000 (1 + 0.042 )10
= 2000 x 1.04510
= 3017.916…
Amount = £3017.92 (nearest pence)
Kate invests £S at 0.35% per month.
Example
The amount after n years is P = S  1.0035 12n
a) Kate invests £6000. Find the amount at the end of 1 year.
b) Hence find the AER.
a) P = 6000  1.003512 = 6256.908…
Amount at the end of 1 year = £6256.91 (nearest pence)
b) AER =
Interest earned in 1 year
 100%
Amount at the beginning of the year
= 256.91  100%
6000
AER = 4.28%
Example
R=
n
A
P
–1
An investment of £3500 has grown to £4600 in 4 years.
Find the annual percentage rate of interest.
R=
=
4
4
4600
3500
–1
1.31428...
–1
= 1.07071... – 1
= 0.07071...
Annual % rate = 7.07% (to 3 sf)