MGT411 ASSIGNMENT 1 SOLUTION 2023 | MGT411 ASSIGNMENT 1 FALL 2023 | MGT411 ASSIGNMENT 1 2023 | MONEY & BANKING | VuTech

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Question No. 1:

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 values for the given scenarios using the compound interest formula:

The compound interest formula is given by:

A = P (1 + r / n​)^nt

Where:

• A is the future value of the investment/loan, including interest.

• P is the principal amount (initial deposit).

• r is the annual interest rate (as a decimal).

• n is the number of times that interest is compounded per year.

• t is the number of years the money is invested/borrowed for.

Now, let's calculate for each scenario:

Scenario 1: Compounded Annually

A =10000 × (1 + 0.08 / 1​ )^(1×6)

Scenario 2: Compounded Semi-Annually

A =10000 × (1 + 0.08 / 2 ​)^(2×6)

Scenario 3: Compounded Quarterly

A =10000 × (1 + 0.08 / 4​ )^(4×6)

Now, let's calculate each scenario.

Scenario 1: Compounded Annually

A₁​ = 10000 × (1 + 0.08 )⁶

Scenario 2: Compounded Semi-Annually

A₂ ​= 10000 × (1 + 0.04 )¹²

Scenario 3: Compounded Quarterly

A₃ ​= 10000 × (1 + 0.02 )²⁴

Now, let's calculate these values:

Scenario 1: Compounded Annually

A₁​ = 10000 × (1.08)⁶

A₁ ​≈ 10000 × 1.5938

A₁ ​≈ 15938

Scenario 2: Compounded Semi-Annually

A₂ ​= 10000 × (1.04)¹²

A₂ ​≈ 10000 × 1.5939

A₂​ ≈ 15939

Scenario 3: Compounded Quarterly

A₃ ​= 10000 × (1.02)²⁴

A₃ ​≈ 10000 × 1.5942

    A₃ ​≈ 15942

Explanation:

Compounding refers to the process where the interest earned on an investment, both the principal and the interest accumulated, earns interest in subsequent periods. The more frequently interest is compounded, the higher the future value of the investment.

In our case:

Compounding annually (Scenario 1) gives a future value of Rs. 15938.

Compounding semi-annually (Scenario 2) gives a future value of Rs. 15939.

Compounding quarterly (Scenario 3) gives a future value of Rs. 15942.

The more frequent compounding leads to a slightly higher future value due to interest being calculated more frequently, resulting in a compounding effect. This demonstrates the impact of compounding frequency on the future value of the investment.

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