Financial Mathematics → Interest → Simple Interest → Compound Interest → Varying Interest Rate → Interest for different Compounding Periods
Financial Institutions often pay or charge interest more than a single time per year. For example, monthly, quarterly, weekly etc.
If the sum of C is invested for a term h at time t. Then the accumulated sum at t+h will be
Where,
C = Original cash
h = Compounding period
ih(t) = Nominal interest rate per annum
A = Accumulated amount
The value of h
Term | h | Reason |
daily | 1/365 | There are 365 days in one year |
weekly | 1/52 | There are 52 weeks in one year |
monthly | 1/12 | There are 12 months in one year |
quarterly | 1/4 | There are 12 months in one year |
biannually | 1/2 | Two times in one year |
Example 1. The nominal interest rate is 12% per annum on transactions of term a month (interest compounded monthly). Calculate the accumulation of $100 invested at this rate after:
(a) 1 month
(b) 2 months
(c) 3 months
Solution:
(a) after 1 month
Answer
(b) after 2 months
Answer
(c) after 3 months
Answer
Example 2. The nominal interest rate of interest per annum quoted in the financial press for local authority deposits on a particular day are as follows:
Term | Nominal rate of interest (%) |
1 day | 11.75 |
1 week | 11.5 |
1 month | 11.375 |
1 quarter | 11.25 |
Find the accumulation of an investment at this time of $100 for
(a) for 2 days
(b) for 3 weeks
(c) for 1 month
(d) for 7 days, and compare with 1 week
(e) for 90 days, and compare with 1 quarter
Solution:
(a) for 2 days
Answer
(b) for 3 weeks
Answer
(c) for 1 month
Answer
(d) for 7 days |
for 1 week |
(e) for 90 days |
for 1 quarter |
Next: Continuous Interest