Cumulative Interest

Cumulative interest is the sum of all interest payments made on a loan over a certain time 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 principal and a lower percentage of its 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 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 available 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: FV = PV x (1 + (i / n)) ^ (n x t)

FV = Future value of money

PV = Present value of money

i = interest rate

n = number of compounding periods per year

t = number of years

While cumulative interest is additive, compound interest can be thought of as “interest on interest.” The formula is as follows:

Compound Interest = Total amount of Principal and Interest in future (or Future Value) less Principal amount at present (or Present Value)

                      = [P (1 + i)n] – P

                      = P [(1 + i)n – 1]

(Where P = Principal, i = nominal annual interest rate in 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 simple interest, which is calculated only on the principal amount.

While cumulative interest is one method of calculating how well a bond investment is performing, the following are more comprehensive yield methods: nominal yield, current yield, effective annual yield, and yield to maturity.