Daily Compound Interest Formula

Daily Compound Interest Formula

In Daily Compound Interest Formula, every period’s interest is calculated based on the prior period’s amount. As a result, the previous period’s principal becomes the current period’s principal. “Compounding” is the process of adding interest to a principal amount.

Daily Compound Interest Formula

In other words, compound interest is the interest added to the principal sum of a loan or deposit. As a result, interest is reinvested, or added to the loaned capital instead of being paid out or required from the borrower, so that interest is earned on both the principal and the previously accumulated interest in the next period. The Daily Compound Interest Formula is a standard concept in finance and economics.

The concept of the Daily Compound Interest Formula is contrasted with simple interest, which does not compound previously accumulated interest to the principal amount of the current period. Multiplying the interest amount per period by the number of periods per year yields the simple annual interest rate. Simple annual interest rates are also known as nominal interest rates (not to be confused with interest rates not adjusted for inflation by the same name).

What is Daily Compound Interest Formula?

Compounding frequency refers to how frequently (or rarely, another unit of time) the accumulated interest is paid out or capitalised (credited to the account). It can be done annually, half-yearly, quarterly, monthly, weekly, daily, or continuously (until maturity).

With a monthly capitalisation and interest expressed as an annual rate, the compounding frequency is 12 and the time periods are measured in months.

Compounding has the following effects:

1. It is the nominal interest rate that is applied
2. The frequency interest is compounded.

Loans with different compounding frequencies cannot be directly compared on the basis of the nominal rate. Comparing interest-bearing financial instruments requires both the nominal interest rate and the compounding frequency.

Many countries require financial institutions to disclose the annual compound interest rate based on Daily Compound Interest Formula on deposits and advances on a comparable basis so that consumers can more easily compare retail financial products. Different markets refer to annual equivalent interest rates as effective annual percentage rates (EAPR), annual equivalent rates (AER), effective interest rates, effective annual rates, and annual percentage yields. In order to calculate the effective annual rate, divide the total accumulated interest up to the end of one year by the principal.

These rates are usually defined in two ways:

1. In this case, the rate is the annualised compound interest rate, and
2. Interest may not be the only charge. Fees and taxes that the customer is charged and which are directly related to the product may be included. Fees and taxes are included or excluded differently in different countries, and may or may not be comparable between jurisdictions due to inconsistent terminology and local practices.

Solved Examples

Example 1: One has invested $1000 in a bank where the amount gets compounded daily at an interest rate of 5%. Then what is the amount one gets after 10 years?
Solution:
To find: The amount after 10 years.
The principal amount is P = $1000.
The interest rate is 5% = 5/100 = 0.05.
t = 10 years.
Using the Daily Compound Interest Formula is:
A = P (1 + r / 365)365 t
A = 1000 ( 1+ 0.05/365)365×10
A =$1648.66
The amount after 10 years is $1648.66.

Practice Questions on Daily Compound Interest Formula

Example 1: How long does it take for $15000 to double if the amount is compounded daily at 10% annual interest? Calculate this by using the Daily Compound Interest Formula and round the answer to the nearest integer.
To find: The time it takes for $15000 to double.
The principal amount, P = $15000.
There is an interest rate of 10% = 10/100 = 0.1.
Based on the assumption that t is the required time in years, the final amount is: A = 15000 × 2 = $30000. Let the required time in years is t.
Using the Daily Compound Interest Formula is:
A = P (1 + r / 365)365 t
30000 = 15000 (1 + 0.1 / 365)365 t
Dividing both sides by 15000,
2 =(1.0002739)365 t
Taking ln on both sides
t = ln 2/(365 ln 1.0002739)
t= 7
Answer: It takes 7 years for $15000 to become double.