Interest is the amount that a borrower pays to a lender or investor in addition to the original sum borrowed. The questions from this topic are easy to solve and can help improve one’s score.

Interest has two major types: Simple Interest and Compound Interest.

**Simple Interest**

The method of calculating the amount of interest charged on a sum at a given rate for a certain period of time is called Simple Interest. It is the easiest way to calculate the additional money one must pay while repaying a loan. It is denoted by SI. This concept is an intrinsic part of banking and finance. In this process, the interest always applies to the original principal amount, with the same rate of interest for every time cycle.

Simple Interest is calculated by using the following formula:

**Simple Interest = **Principal X Rate of Interest X Time100 = P R T100

Where

**Principal =**The amount originally borrowed. It is denoted by**P**.**Rate =**The rate of interest at which the principal amount is provided for a certain period. It is denoted by**R**.**Time =**The duration of repayment of the principal amount with a mentioned rate of interest. It is denoted by**T**.

**Amount: **The total sum which is repaid to the lender is called the **amount**. It includes the money borrowed and the interest levied on it and is denoted by **A**. Amount can be calculated by using the following formulas:

**Amount = Simple Interest + Principal**

**A = **SI + P , **A = **P + PRT100 **= **P1 + RT100

**Compound Interest**

The method of charging interest on the principal amount and the cumulative interest from previous time cycles is called compound interest. Depending on the number of compounding periods, compound interest is calculated. Therefore, as the number of compounding periods increases, the amount of interest charged also increases. Nowadays, most banks adhere to the compound interest method as it increases the revenue generated by lending. Compound interest is denoted by ‘CI’.

The formula used to calculate compound interest is

**CI = **P1+ rnnt– P

And the final amount can be calculated by

** A =** P1+ rnnt

Where

- P is the initial principal amount
- r is the rate of interest
- n number of times interest applied per time period
- t total time duration

In the case of compounding annually, the formulas are:

**CI = **P1+ r100t– P, **A =** P1+ r100t

**Sample Questions **

- Alex invests $100,000 in an account that pays 12% annual interest: the interest is paid once, at the end of the year. Mary invests $100,000 in an account that pays 12% annual interest, compounding monthly at the end of each month. At the end of one full year, compared to Alex’s account, approximately how much more does Mary’s account have?

- Zero
- $68.25
- $682.50
- $6825.00
- $68250.00

**Answer: C**

**Explanation:**

Given that,

Alex invests $100,000 in an account that pays 12% annual interest. It is simple interest.

Simple Interest = Pnr100

Alex’s interest = $100,000*0.12*1 = $12,000 for one year or $1,000 each month.

Simple Interest = Pnr100

Also given that,

Mary invests $100,000 in an account that pays 12% annual interest, compounding monthly at the end of each month

C.I = {P1+r100n-P }

Where P-PrincipalInitial sum, r-rate of interest and n-no. of years

C.I = {1000001+0.121212-100000 }

= {1000001+0.121212-1

= {1000001.0112-1

= 112682.50 -100000 = 12682.50 $

So, Mary and Alex’s difference amount = 682.5.

We can use the above formula, but raising to the power of 12 is not easy to calculate. Let’s break it down to smaller values.

**Logical explanation:**

Mary’s interest, 12%/12 = 1% each month:

For the 1st month = $100,000*0.01 = $1,000;

For the 2nd month = $1,000 + 1% of 1,000 = $1,010, so we would have interest earned on interest (very small amount);

For the 3rd month = $1,010 + 1% of 1,010 = ~$1,020;

For the 4th month = $1,020 + 1% of 1,020 = ~$1,030;

…

For the 12th month = $1,100 + 1% of 1,100 = ~$1,110.

The difference between Alex interest and Mary’s interest = ~ (10 + 20 + … + 110) = $660.

**Hence, the answer is C.**

2. Beck made an investment of $1,000 and earned interest that was compounded annually. The annual interest rate was constant for the duration of the investment, and after 12 years the $1,000 increased to $4,000 by earning interest. In how many years after the initial investment was made would the $1,000 have increased to $8,000 by earning interest at that rate?

- 16
- 18
- 20
- 24
- 30

**Answer: B**

**Explanation: **

Given,

Beck made an investment of $1,000 and earned interest that was compounded annually.

We know that,

C.I = {P1+r100n-P }

Where P – Principal (Initial sum), r – rate of interest and n – no. of years.

Total Amount = {P1+r100n }

After 12 years the $1,000 increased to $4,000 by earning interest.

Total Amount = {10001+r10012 }=4000

1+r10012 =4

Taking 12th root on both sides.

1+r1001=4112……………………….(1)

**Question: **In how many years after the initial investment was made would the $1,000 have increased to $8,000 by earning interest at that rate?

Let “n” be the no. of years.

Then,

Total Amount = {10001+r100n }=8000

1+r100n =8

Using equation (1)

4^(112)n =8

2n6=23

So,

n6=3

n = 18.

**Hence, the answer is B.**

**Logical Explanation:**

In 12 years, the investment quadrupled (from $1,000 to $4,000).

Thus, at the same rate compounded annually, it would need additional 12/2=6 years to double (from $4,000 to $8,000).

Therefore, 12+6=18 years are needed $1,000 to increase to $8,000.

**Hence, the answer is B.**