## What is accrued interest?

Accumulated interest is the sum of all interest payments made on a loan over a certain period. On a depreciable loan, the cumulative interest will increase at a decreasing rate, as each subsequent periodic payment on the loan is a higher percentage of the loan amount main and a lower percentage of its stake.

## Use of accrued interest

The accrued interest is sometimes used to determine which loan in a series is the most economical. However, the accrued interest alone does not take into account other important factors, such as the initial costs of the loan (if a lender pays these costs out of pocket rather than carrying them over to the loan balance) and the the time value of money.

The Time Value of Money (TVM), also known as the current discount rate, is a central concept in finance. It focuses on the idea that the money available now is worth more than the same amount in the future, due to its potential earning power. Provided that money can earn interest, any amount is worth the sooner it is received.

The general formula for TVM is: FV = PV x (1 + (i / n)) ^ (nxt)

FV = Future value of money

PV = present value of money

i = interest rate

n = number of compounding periods per year

t = number of years

## Cumulative interest vs compound interest

Although the cumulative interest is additive, compound interest can be considered as “interest on interest”. The formula is as follows:

Compound interest = Total amount of capital and future interest (or future value) less Current principal amount (or present value)

= [P (1 + i)n] – P

= P [(1 + i)n – 1]

(Where P = Principal, I = nominal annual interest rate as a percentage, and n = number of compounding periods.)

For example, how much would interest be on a five-year, \$ 10,000 loan at a 5% interest rate compounded annually? In this case, it would be: \$ 10,000 [(1 + 0.05)5] – 1 = \$ 10,000 [1.27628 – 1] = \$ 2,762.82.

Selecting compound interest will grow a sum faster than simple interest, which is calculated only on the principal amount. This happens because, when the interest is compounded, the money earned from the interest is added to the principal periodically, so that more interest is earned in the next period. This process repeats itself, leading to larger earnings due to interest.

## Accumulated interest and bond yield measures

While accrued interest is one method of calculating the performance of a bond investment, here are more comprehensive return methods: nominal yield, current yield, effective annual yield, and yield to maturity.

## Example of cumulative interest

Accumulated interest is all interest earned or paid over the life of a security or loan, added together. If you borrowed \$ 10,000 at an interest rate of 3% per year, you would pay \$ 300 in interest in the first year. If you paid \$ 1,200 in the first year and owed only \$ 8,800 in the second year, your interest for the second year would be \$ 264. Your cumulative interest for years one and two would be \$ 564.