Compounding Quarterly Formula

What is Quarterly Compounding?

Compounding quarterly can be considered as the interest amount 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 banks offer interest income on the deposits, which compound quarterly. Further, it can be used to calculate any income on other financial products or money market instruments offering quarterly income.

Quarterly Compounding Formula

C_q = P [ (1+r)^4*n – 1 ]

You are free to use this image on your website, templates, etc., Please provide us with an attribution linkHow to Provide Attribution?Article Link to be Hyperlinked
For eg:
Source: Compounding Quarterly Formula (wallstreetmojo.com)

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 formulaCompounding FormulaCompounding is a method of investing in which the income generated by an investment is reinvested, and the new principal amount is increased by the amount of income reinvested. Depending on the time period of deposit, interest is added to the principal amount.read more. Here the principal amount, number of periods, and the interest rate 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 four 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 deposited includes a premium of 11,000 for scheme one, which shall not be invested, and scheme II, which 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 would be 200,000 less 11,000, which is 189,000 for scheme I, and for scheme II it would be 400,000 less 25,000, which is 375,000.

Use the following data for the 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 six years, and another is for seven years. Further, if we go through policy benefits, the customer might choose scheme I as a lower investment and policy cover of 1000,000.

Example #3

SMC Municipal corporation has issued 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 formula below to calculate the income derived by investing 10,000 monthly for 12 years at a rate of 11.50% compounded monthly.

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