FINANCE
APPRECIATION:
SIMPLE INTEREST COMPOUND INTEREST
A = P(1+i.n) A = P(1+i)ⁿ
Calculated on the principal or original amount Calculated on the principal amount, and also on
of a loan. the accumulated interest of previous periods –
regarded as “interest on interest”.
A = Final Amount
P = Principal/Initial Amount
m = Compounding Period
n = Number of Years
COMPOUNDING PERIODS:
Frequency of compounding Number of times interest is Interest rate
added during a year (n)
Annual 1 (every year) – n i
Semi-annual 2 (every 6 months) – n x 2 i/2
Quarterly 4 (every 3 months) – n x 4 i/4
Monthly 12 (every month) – n x 12 i/12
Daily 365 (every day) – n x 365 i/365
When we calculate interest for different compounding periods, we must adjust i and n accordingly.
For example: If we compound quarterly, we divide the interest rate by 4 to give us the rate per
quarter and we multiply the number of years by 4 to give us the number of quarters.
( )
n.m
i
A=P 1+
m
NOMINAL AND EFFECTIVE INTEREST RATES:
Nominal interest rate (nom) – One where the interest rate quoted, and the compounding
periods are different.
Effective interest rate (eff) – One where the interest rate quoted, and the compounding
periods are the same.
Formula to convert one to the other (not given on formula sheet):
( )
m
1 i nom
( 1+ieff ) = 1+ m
inom is the interest rate p.a. compounded m times in 1 year.
When converting from a nominal (nom) to an effective (ieff) rate, or vice versa, we perform our
calculations for a period of 1 year only, irrespective of the period stated.
APPRECIATION:
SIMPLE INTEREST COMPOUND INTEREST
A = P(1+i.n) A = P(1+i)ⁿ
Calculated on the principal or original amount Calculated on the principal amount, and also on
of a loan. the accumulated interest of previous periods –
regarded as “interest on interest”.
A = Final Amount
P = Principal/Initial Amount
m = Compounding Period
n = Number of Years
COMPOUNDING PERIODS:
Frequency of compounding Number of times interest is Interest rate
added during a year (n)
Annual 1 (every year) – n i
Semi-annual 2 (every 6 months) – n x 2 i/2
Quarterly 4 (every 3 months) – n x 4 i/4
Monthly 12 (every month) – n x 12 i/12
Daily 365 (every day) – n x 365 i/365
When we calculate interest for different compounding periods, we must adjust i and n accordingly.
For example: If we compound quarterly, we divide the interest rate by 4 to give us the rate per
quarter and we multiply the number of years by 4 to give us the number of quarters.
( )
n.m
i
A=P 1+
m
NOMINAL AND EFFECTIVE INTEREST RATES:
Nominal interest rate (nom) – One where the interest rate quoted, and the compounding
periods are different.
Effective interest rate (eff) – One where the interest rate quoted, and the compounding
periods are the same.
Formula to convert one to the other (not given on formula sheet):
( )
m
1 i nom
( 1+ieff ) = 1+ m
inom is the interest rate p.a. compounded m times in 1 year.
When converting from a nominal (nom) to an effective (ieff) rate, or vice versa, we perform our
calculations for a period of 1 year only, irrespective of the period stated.
