Suppose you have a saving account in Bank XYZ and you have deposited an amount of Rs.10,000 into your account on January 01, 2018. The rate of interest that bank pays on deposits is 8% per annum. Requirements: 1. If the interest rate compounds annually then how much amount will you have on January 01, 2024 in your account? 2. If the interest rate compounds semi-annually then how much amount will you have on January 01, 2024 in your account? 3. If the interest rate compounds quarterly then how much amount will you have on January 01, 2024 in your account? 4. Supporting the results of above three requirements; you are required to explain compounding and the effect of compounding frequency on future value of your investment. NOTE: It is required to show complete calculation along with formulas.

Suppose you have a saving account in Bank XYZ and you have deposited an amount of Rs.10,000 into your account on January 01, 2018. The rate of interest that bank pays on deposits is 8% per annum.

Requirements:

1. If the interest rate compounds annually then how much amount will you have on January 01, 2024 in your account?

2. If the interest rate compounds semi-annually then how much amount will you have on January 01, 2024 in your account?

3. If the interest rate compounds quarterly then how much amount will you have on January 01, 2024 in your account?

4. Supporting the results of above three requirements; you are required to explain compounding and the effect of compounding frequency on future value of your investment.

NOTE: It is required to show complete calculation along with formulas.

Solution:

let's calculate the future value of the investment under different compounding scenarios.

Requirement 1: Annually Compounded Interest

The formula for future value with annual compounding is given by:

`FV=P×(1+r/n)^nt`

Where:

• FV is the future value of the investment,

• P is the principal amount (initial deposit),

• r is the annual interest rate (in decimal form),

• n is the number of times interest is compounded per year, and

• t is the number of years.

Given values:

P=Rs.10,000,

r=8%=0.08,

n=1 (compounded annually),

t=6 years (from 2018 to 2024).

` FV_1 =10000×(1+0.08/1)^{1×6}`

Requirement 2: Semi-annually Compounded Interest

For semi-annual compounding, n=2.

`FV_2 =10000×(1+0.08/2)^{2×6}`

 

Requirement 3: Quarterly Compounded Interest

For quarterly compounding, n=4.

`FV_3=10000×(1+0.08/4)^{4×6}`

Calculations

Let's calculate these values:

FV1 =10000×(1+0.08/1)6

FV2 =10000×(1+0.08/2) 12

FV3=10000×(1+0.08/4)24 

Explanation

The concept of compounding refers to the process where the interest on an investment earns interest over time. The more frequently interest is compounded, the more the investment grows.

Annual Compounding: Interest is added once a year.

Semi-annual Compounding: Interest is added twice a year.

Quarterly Compounding: Interest is added four times a year.

As compounding frequency increases, the future value of the investment tends to be higher because interest is being calculated more frequently and added to the principal, leading to more significant overall growth. This effect is known as the compounding effect.