# Interest

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:

$I=niC$

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
$I=niC \\ =(1)(0.05)(1000) \\ = \50$

(b) After 2.5 years
$I=niC \\ =(2.5)(0.05)(1000) \\ = \125$

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
$I=niC \\ =(50/365)(0.1)(1000) \\ =\13.7$

(b) After 20 weeks
$I=niC \\ =(20/52)(0.1)(1000) \\ =\38.46$

(c) After 8 months
$I=niC \\ =(8/12)(0.1)(1000) \\ =\66.67$

Next: Simple Interest

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