Higher Algebra Hall & Knight Interest & Annuities (Chapter 18) Solutions

Hall and Knight Higher Algebra Chapter 18 ‘Interest and Annuities’ are the best study resources available for JEE and NEET aspirants. With the help of these solutions, you will be able to solve questions connected with interest and discount may be simplified by the use of algebraic formula. We shall use the term interest discount to solve the chapter-related questions. The chapter consists of crucial concepts like meaning of interest, discount, and personal value, what is compound interest, definition of annuities, life annuity, perpetuity, deferred perpetuity and freehold estate. 

There is a total of 2 exercises in the Higher Algebra by Hall and Knight Chapter 18 ‘Interest and Annuities’. These exercises contain 25 questions that are unsolved for conditioning your skills. The first exercise consists of questions based mainly on the concept of compound interest. In the second exercise, the questions include topics like simple interest and discount. All the questions are very essential as they will clarify your previously learned concepts about interest and will introduce you to new concepts of Annuities. 

Instasolv’s Hall & Knight Algebra Mathematics book with solutions is perfect to study for JEE Mains and JEE Advanced exams. In order to save your time and effort in case you get confused at some point, Instasolv provides you with easy access to the solutions all the time. All the solutions are written step by step so that you find it easy to understand this chapter. 

Important Topics in Hall & knight Higher Algebra Solutions Chapter 18: Interest and Annuities


Interest is the cost that is charged by the moneylender. When you borrow an amount from someone, interest is basically the cost that you pay for using someone else’s money. If you are the lender then the interest is earned by you but if you are the borrower you have to pay the interest.

A simple Interest can be calculated by multiplying the principal amount with one plus the rate of interest for a particular time period. The formula is written as A = P(1+rt).


A discount refers to the price offered which is lower than the actual price or face value of a product. In simple words, a discount is a reduction in a product’s cost price.

A discount can be calculated by subtracting the price post the discount with the before discount price, then divide the new numbers by the actual price and multiply the result by 100. 

What is compound interest?

Compound interest is mainly known as interest on interest which means it refers to the addition of interest to the principal sum of a deposit or loan. It is basically the conclusion or the result of reinvesting rather than paying it out. Therefore, the final interest in the next period is earned on the principal sum with the addition of the previously accumulated or combined interest.

We can calculate compound interest by multiplying the initial principal amount by adding 1 to the annual rate of interest raised to the number of compound periods subtracted by 1. Compounded interest can be calculated on any given frequency schedule that might be daily to annually.

The formula of compound interest is A = P(1+r/n)nt.


An annuity is basically a payment made monthly or yearly. We witness annuity in our everyday life when we pay an amount on a regular basis and mostly the amount remains the same. Some of the common examples of annuity are bank loans, house loans, insurance, apartment rents, etc. 

To conclude we can say that annuity is just a payment system that takes place in a specific period of time. An annuity is of two types- annuity regular and annuity due which is also known as annuity immediate.

Life Annuity

A life annuity is in simple terms, is annuity i.e payments made in a period of time while the annuitant or the purchaser is alive. A life annuity can be paid once and for all which is a single-payment annuity or a series of regular payments. 


It is a special version of the annuity. Perpetuity involves the receipts that take place for more than the usual time period. Therefore, a deferred or delayed perpetuity is a type of perpetual stream of cash that flows and begins at a predetermined date in the future.

Freehold Estate

Freehold estate is an estate that allows you to enjoy the possession of a property without mentioning a particular period of time. There are three types of freehold estate which are fee simple, a fee tail, and a life estate. 

Exercise Discussion of Hall & Knight Higher Algebra Solutions Chapter 18: Interest and Annuities

  • Higher Algebra By H.S. Hall and S.R. Knight Chapter 18 ‘Interest and Annuities’ has 2 exercises with 25 questions in total. 
  • In the first exercise, there are just 10 questions that are framed according to the chapter’s concept of compound interest. While solving this exercise, you will face questions like finding the amount of the given money in fifty years at 5 per cent compound interest and given log, in how many years will a sum of money double itself at 5% compound interest, etc.
  • In the second exercise, there are 15 questions. These questions are based on the concept of rate interest, simple interest as well as compound interest. For instance, one question asks if a person borrows a sum of money that has to be repaid in 5 years by annual statements then what would be the rate of interest reckoning simple interest. 
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