Question #210296

Qno # 1 You are a CEO of a company and your company wants to invest $100,000 for the period of five years. One bank name HBL offers interest rate of 5% for the period of 5 years. While other bank name ABL offers the compound interest rate of 4% semi-annually. Being CEO of company what will be your decision either you will invest in HBL or ABL based on the future value of money.

Expert's answer

The future value of an investment represents the initial value invested plus accumulated interest earned thereon at a given rate. The future value of a single sum can be determined using the following formula:

"future \\space value=present\\space value\\times(1+r)^n"

*Where:*

*The initial investment amount is treated as present value, *

*The periodic interest rate is denoted by r, and *

*The number of periods of the investment is denoted by n.*

The nominal annual interest rate is the rate stated on a financial contract to calculate periodic interest payments, but it is not the actual interest income or expense because it does not consider the compounding effect. The effective annual interest represents the true picture of interest because it considers the compounding effect occurring during a particular period.

In order to analyze both alternatives, we need to calculate the expected future value of the initial investment after five years.

Calculating the future value in the case of HBL bank:

"future \\space value=present\\space value\\times(1+r)^n\\\\=100000\\times(1+0.05)^5\\\\=\\$127628.16"

*Where:*

the present value of investment=$100000,the effective annual rate(r)=0.05 and the number of annual period(n)=5

Calculating the future value in the case of ABL bank:

"future \\space value=present\\space value\\times(1+r)^n\\\\=100000\\times(1+0.02)^{10}\\\\=\\$121899.44"

*Where:*

the present value of investment=$100000

the effective semi-annual rate(r)"\\frac{0.04}{2}=0.02"

the number of semi-annual period(n)"=5\\times2=10"

the number of compounding per year=2

Conclusion:** The company should invest in HBL bank because it is providing higher future value as compared to the ABL bank. **

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