Compounding Quarterly Formula

What is Quarterly Compounding?

Compounding quarterly can be considered as the interest amount which is earned quarterly on an account or an investment where the interest earned will also be reinvested. and is useful in calculating the fixed deposit income as most of the banks offer interest income on the deposits which compound quarterly. Further, it can also be used to calculate any income on other financial products or money market instruments that offer quarterly income.

Quarterly Compounding Formula

Where,

• C_q is the quarterly compounded interest
• P would be the principal amount
• r is the quarterly compounded rate of interest
• n is the number of periods

The formula for compounding quarterly is a subset of compounding formula. Here the principal amount, number of periods, rate of interest would be required. The only modification is the rate of interest would be raised to n*4, which is static since we are supposed to calculate interest quarterly. Therefore, it compounds the interest quarterly, and the income grows every quarter, which is what this formula is trying to explain and get those results.

Examples

Example #1

Mr. Kamal deposited $50,000 in KJK bank for 4 years, and the bank pays 5 percent as a rate of interest, which is quarterly compounded. You are required to calculate the quarterly compounded interest.

Solution

We are given all the required variables;

• Principal Amount: 50000.00
• Rate of Interest: 5%
• Number of Years: 4.00
• Frequency: 4.00

Therefore, the calculation of quarterly compound interest will be –

• C_q = P [ (1+r)^4*n – 1 ]
• =  50,000 [ (1+5%/4)^4*4 – 1 ]
• = 50,000 [ (1.0125)¹⁶ – 1 ]

• =  10,994.48

Example #2

BCC co-operative bank has two schemes which they are evaluating the projections as to which would be more preferred by their customers. The details of both schemes are given below, as collected by the finance department.

Particulars	Scheme I	Scheme II
Initial Amount to be Deposited	200,000	400,000
Rate of Interest	8.50%	8.25%
Minimum Lock-in Period	6	7
Compounded Frequency	4	4
Additional Benefit	Life Insurance	Medical Insurance

The initial amount that is deposited includes a premium of 11,000 for scheme one, which shall not be invested, and for scheme II there is a premium of 25,000, which shall not be invested. Life Insurance covers the benefit of 1000,000, whereas the medical scheme covers the benefit of 700,000.

You are required to evaluate the benefits of the scheme.

Solution

Here, we need to compare the scheme benefits, and first, we shall calculate the quarterly compounded interest.

The initial amount that would be invested will be 200,000 less 11,000, which is 189,000 for the scheme I, and for scheme II it would be 400,000 less 25,000, which is 375,000.

Use the following data for calculation of quarterly compound interest

Scheme I

• C_q =  P [ (1+r)^n*4 – 1 ]
• =189,000 [ (1+(8.50%/4))^(6*4) – 1 ]
• =189,000 [ (1.02125)²⁴ – 1 ]

• = 1,24,062.81

Scheme II

• C_q =  P [ (1+r)^n*4 – 1 ]
• = 375,000 [ (1+(8.25%/4)^(7*4) – 1 ]
• =  375,000 [ (1.020625)²⁸ – 1 ]

• = 2,89,178.67

It is difficult to make a decision here as we are not comparing apples to apples as one scheme is for 6 years and another one is for 7 years and further, if we go through policy benefits then the customer might choose scheme I as lower investment and policy cover of 1000,000.

Example #3

SMC Municipal corporation has issue new products for capturing money from the market. Money has to be invested in two phases. In phase I, 50% will be invested, and the rest will be invested after five years. For the first five years, the rate of interest that will be paid is 8%, and for the next five years, it will be 7.5%. These will be paid quarterly. Mr. W invested 500,000 in the initial period.  You are required to calculate the income earned on the investment for Mr. W.

Solution

We are given all the details here, and we can use the below formula to calculate the income that will be derived by investing 10,000 monthly for 12 years at a rate of 11.50% compounded monthly.

Use the following data for calculation of quarterly compound interest

Particulars	Phase I	Phase II
Principal Amount (P)	2500.00	2500.00
Rate of Interest (r)	8.00%	7.50%
Number of Years (n)	5	5
Frequency	4	4

Phase I

• C_q =  P [ (1+r)^n*4 – 1 ]
•   =  250,000 [ (1+(8.00%/4)^(4*5) – 1 ]
• =  250,000 [ (1.02)²⁰ – 1 ]

= 1,21,486.85

Phase II

• C_q = P [ (1+r)^n*4 – 1 ]
• =  250,000 [ (1+(7.50%/4)^(4*5) – 1 ]
• =250,000 [ (1.01875)²⁰ – 1 ]

= 1,12,487.01

Total Income 

Hence, the total income earned by Mr. W on his investment will be 1,21,486.85 + 1,12,487.01 which shall be 2,33,974.

Relevance and Uses

Compounding can be monthly, quarterly, semi-annually, and annually and most of the financial products, which include saving accounts as well, are mostly based on a quarterly or semi-annually basis. Compounding grows the money much faster than the interest which is earned by way of simple interest. 

This article has been a guide to Compounding Quarterly Formula. Here we discuss the calculation of quarterly compounded interest along with practical examples and downloadable excel templates. You may learn more about finance from the following articles –

• How to Calculate Value of Fixed Deposit?
• Examples of Compound Interest
• Daily Compound Interest
• Formula of Continuous Compounding
• Normalization Formula