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Financial Mathematics

• Terminology related to simple interest:
1. The amount of money that is borrowed is known as principal and is denoted by P.
2. The extra amount of money that one has to pay is known as interest and is denoted by I.
3. The total amount of money, A that one pays back is equal to the sum of principal and interest.
4. The simple interest (SI) on the principal (P) when borrowed for T years at R% rate of interest per year is given by the formula

Example

Rashmi takes a loan of Rs 4000 from a bank at 8% rate of interest per year. Find the amount of money that Rashmi has to repay after 3 years.

Solution

P = Rs 4000, R = 8% p.a., T = 3 years

∴ Amount = P + I = Rs 4000 + Rs 960 = Rs 4960

Thus, Rashmi has to repay Rs 4960 after 3 years.

Note: Principal remains unchanged throughout the given time period while calculating the simple interest.

COMPOUND INTEREST

In compound interest transactions, interest is compounded into principle after each period, which can be a year, a half-year, a quarter-year, a month, or any other time interval. This means that at the end of the first period, the sum (principal + interest) becomes the principal for the second period.

The principal for the third period is equal to the amount at the end of the second period, and so on. The conversion period is the period after which interest is paid each time to produce a new principal. The compound amount is the entire amount owed at the end of the previous period.

The difference between the compound amount and the original principle is called the compound interest and is abbreviated as C.I.

⇒ C.I = Compound Amount $-$ Principal

#Note 1: When interest is compounded annually, the compound interest and simple interest for the first year are the same.

#Note 2: Interest is converted into principal under compound interest, therefore there is interest on principal as well as interest on interest.

#Note 3: The interest rate is usually represented as an annual rate. When the conversion period is not a year, the rate per conversion period is calculated by multiplying the specified annual rate by the number of conversion periods in the year.

Eg., if the quoted rate is 16% compounded quarterly, the rate per conversion period is 4% or 0.04; if no conversion period is specified, interest is converted annually. As a result, the statement "interest at 6% " or "money worth 6%" will imply 6% compounded annually.

COMPUTATION OF COMPOUND INTEREST

Derivation of formulae for computing compound amount (S) and compound interest (C.I).

Theorem 1: Prove that the compound amount S and compound interest C.I. of a principal P at the end of n conversion periods at the intere…

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