Quarterly Compound Interest Formula

Quarterly compound interest formula

When it comes to accumulating assets, the magic of composition can be very beneficial. The previous method was to create a stock option and start saving money. The more money you save, the more money you get through compound interest. 

When interest is calculated quarterly, it is referred to as compound interest. Because one year has four quarters, the rate of interest will be one-fourth of the annual rate, and the time period will be four times the duration specified in years.

As a result, with quarterly interest amount is calculated as:

A=P (1 + r/4100)4n=P 1 + r/4004n 

Compound interest rates accelerate the growth of money. This allows the amount of money to grow at a faster rate than simple interest because the individual receives a return on the same capital he has invested and a return at the end of each compound period. That means they no longer have to make big money to realize their ambitions.

Solved examples:

Question 1: suppose one has invested a principal sum of $1200 in a bank and money is compounding quarterly at 6 and interest is received quarterly. Determine the amount he will receive at the end of 10 years?

Solution:

To find the amount after 10 years.

Given

• P = $1200.

• r = 6% = 6/100 = 0.06.

• t = 10.

With the use of the quarterly compound interest formula:

A = P (1 + r / 4)4 t

A=1200(1+0.015)40

 A=2176.822

 The amount receivable after 10 years = $2176.822

Question 2: How long will it take for an initial sum of $13000 to double up if the sum is being compounded quarterly at an interest rate of 10% annual? Find the answer in integer.

Solution:

For finding the time needed for $13000 to double:

Given details 

• P = $13000.

• r = 10% =10/100 = 0.1.

• A = 13000 x 2 = $26000

Let us make an assumption that the time needed for the sum to double in years is t.

Using the quarterly compound interest formula:

• A = P (1 + r / 4)4t

• 26000=13000 (1+0.14)4t  

• Dividing l.h.s and the r.h.s by 13000 we get

• 2= (1.025)4t 

• Taking LN on both sides ln2=4t ln1.025t

• And t comes out to be 7 year 

• It will take an amount of $13000 to double in 7 years when compound is made quarterly.