What Is Cumulative Interest?

Cumulative interest is the sum of all interest payments made on a loan over a certain period. On an amortizing loan, cumulative interest will increase at a decreasing rate, as each subsequent periodic payment on the loan is a higher percentage of the loan’s 澳洲幸运5开奖号码历史查询:principal and a lower percentage of its interest.

Using Cumulative Interest

Cumulative interest is sometimes used to determine which loan in a series is most economical. However, cumulative interest alone does not account for other important factors, such as initial loan costs (if a lender pays these costs out of pocket as opposed to rolling them over into the loan's balance) and the 澳洲幸运5开奖号码历史查询:time value of money.

The time value of money (TVM), also known as the present discount rate, is a core concept in finance. It centers on the notion that money availabl෴e at present is worth more than the same amount in the future, due to its potential earning capacity. Provided money can earn interest, any amount is worth more the sooner it ﷽is received.

The general formula for TVM is:

$\begin{aligned}&\text{FV}=\text{PV}\times\bigg(1+\bigg(\frac{\text{i}}{\text{n}}\bigg)\bigg)^{(\text{n}\times\text{t)}}\\&\textbf{where:}\\&\text{FV}=\text{Future value of money}\\&\text{PV}=\text{Present value of money}\\&\text{i}=\text{Interest rate}\\&\text{n}=\text{Number of compounding periods per year}\\&\text{t}=\text{Number of years}\end{aligned}$​FV=PV×(1+(ni​))(n×t)where:FV=Future value of moneyPV=Present value of moneyi=Interest raten=Number&nbওsp;of compounding periods&ඣnbsp;per yeart=Number of years​

Cumulative Interest vs. Compound Interest

While cumulative interest is additive, 澳洲幸运5开奖号码历史查询:compound interest can be thought of as “interest on inte⛦reꩵst.” The formula is as follows:

澳洲幸运5开奖号码历史查询:Compound Interest = Total amount of Principal and Interest in future (or Future Value) less Principal amount at present (or🌌 Present Value

     $\begin{aligned}&=[P(1+i)^n]-P\\&=P[(1+i)n-1]\end{aligned}$​=[P(1+i)n]−P=P[(1+i)n−1]​

(Where P = Principal, i = nominal annual interest rate i🍰n percentage terms, and n = number of compounding periods.)

For example, what would the amount of interest be on a five-year loan of $10,000 at an interest rate🔯 of 5% that compounds 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 make a sum grow at a faster rate than 澳洲幸运5开奖号码历史查询:simple interest, which is calculated only on the principal amount. This happens because,♎ when interest is compounde𒁏d, the money earned through interest is added to the principal periodically, so that more interest is earned in the next period. This process repeats itself, leading to larger gains due to interest.

Cumulativeও Interest and Mea𒁏sures of Bond Performance

While cumulative interest is one method of calculating how well a bond investment is performing, the following are more comprehensive yield methods: 澳洲幸运5开奖号码历史查询:nominal yield, 澳洲幸运5开奖号码历史查询:current yield, 澳洲幸运5开奖号码历史查询:effective annual yield, and 澳洲幸运5开奖号码历史查询:yield to maturity.

Cumulative Interest Example

Cumulative 🍒interest refers to all of the 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% annually, you’d pay $300 in interest in the first year. If you paid off $1200 in the first year and only owed $8,800 in year two, your interest for year tw🐟o would be $264. Your cumulative interest for years one and two would be $564.