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