Financial Mathematics → Interest Calculations

The most common investments is the investment of money at interest. When money is deposited in a bank, the bank pays interest as a reward for the use of an asset called “capital”.

Interest Formula
Interest is calculated by the formula:

Where,
I = Interest earned
C = Cash amount (called Capital)
i = Interest rate
n = Time period (in years).

Remember: 5% = 0.05, 7% = 0.07, 10% = 0.1, 15% = 0.15, 20% = 0.2

Example 1. Suppose $1,000 is deposited in a bank that earns 5% interest per annum. What is the amount of interest earned after:
(a) 1 year
(b) 2.5 years

Solution:
(a) After 1 year

(b) After 2.5 years

Important:
If we have annual interest (Like interest rate per annum in the above example). And, we have time period in days, weeks and months then??

Interest for	Time (n)	Reason
1 day	1/365	There are 365 days in one year
5 days	5/365	There are 365 days in one year
1 week	1/52	There are 52 weeks in one year
7 weeks	7/52	There are 52 weeks in one year
1 month	1/12	There are 12 months in one year
6 months	6/12	There are 12 months in one year

As we have interest rate per annum, so we are giving time (n) in terms of years, like, 6/12 for 6 months, 10/12 for 10 months and 12/52 for 12 weeks.

Example 2. Suppose $1,000 is deposited in a bank that earns 10% interest per annum. What is the amount of interest earned after:
(a) 50 days
(b) 20 weeks
(c) 8 months

Solution:
(a) After 50 days

(b) After 20 weeks

(c) After 8 months

Next: Simple Interest