Business Mathematics Case Study: Compound Interest Applications

This document presents a detailed solution to a business mathematics case study, focusing on the application of compound interest formulas to solve various financial problems. The case involves calculating loan amounts, repayment periods, and present values under different interest rate scenarios, including semi-annual and quarterly compounding. Specific calculations are performed to determine the present value of a loan with semi-annual interest, the time required for debt repayment, and the fair value of a loan based on discounted future payments. The solution provides step-by-step explanations and calculations for each question, demonstrating the use of compound interest formulas in practical financial applications. Desklib offers a wealth of similar solved assignments and past papers to aid students in their studies.

Running head: BUSINESS MATHEMATICS
Business Mathematics
Name of the Student:
Name of the University:
Author’s Note:

2BUSINESS MATHEMATICS
Table of Contents
In Response to Question 1...............................................................................................................3
In Response to Question 2...............................................................................................................3
In Response to Question 3...............................................................................................................3
In Response to Question 4...............................................................................................................4
In Response to Question 5...............................................................................................................4
In Response to Question 6...............................................................................................................4
In Response to Question 7...............................................................................................................5
References........................................................................................................................................6

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In Response to Question 1
The loan amount provided by the angel investor could be calculated as the present value of the
amount paid after two years of time. The interest rate applicable for the transaction was around
6% payable semi-annually over the two-year time. The savings of $80,654 will be pulled back
two years back at the semiannual rate of 6% payable semiannually (Eisenberg & Mishura, 2018).
Future Value = 80,654
Interest Rate = 6% payable semiannually.
Time= 2years
Calculated Present Value = 71,660.34
In Response to Question 2
Question 2
Int Rate Compounded Monthly
Future Value 80654
Time (In Years) 12
Interest Rate 5.93%
Int Rate Comp. Semi-Annually
0.00493
8
Factor
1.00493
8
Semi Annual Rate
1.06088
6
Present Value
71661.9
5
In Response to Question 3
It would take around 71 month of time for the repayment and for reaching the debt of $100,000
assuming the interest rate of around 6% payable semiannually. The Present Value considered for

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the calculation was around 71,660 and the N (Time period was calculated using the back
calculation for solving the same).
In Response to Question 4
Question 4
Future Value 80654
Time (In Years) 1.5
Interest Rate 8%
Int Rate Comp. Semi-Annually
0.041006
7
Factor
1.041006
7
Semi Annual Rate 1.062
Present Value (Value of the
Loan) 71660.03
In Response to Question 5
Question 5
Future Value 80654
Time (In Years) 2
Interest Rate 6%
Int Rate Comp. Annually 6%
Factor 1.06
Semi Annual Rate 1.1236
Present Value (Value of the
Loan)
63885.52
2
In Response to Question 6
If the contract was for two years of time and the loan had to be settled in the same amount of
time then the following amount 25,000 and 40,000. It would be repaid at the respective year end
would be discounted at the todays rate at the all in interest rate of 6% to determine the fair value

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of the loan amount that can be granted. The final amount calculated for the loan amount was
around $59,184.76 as the total amount (Xiong et al. 2016).
In Response to Question 7
The final amount of $80,654 will be pulled back at the respective mentioned period of two years
with the rate of 6% compounded semiannually and 8% compounded quarterly. The rate
calculated for the first year was 6.09% and the return for the second year was calculated to be
around 8.24% that was the return calculated on a quarterly compounded basis.
The amount for the second year will be calculated as = (80,654/ (1.0824)) = 74,514.
The amount derived for the second year will then be pulled back for the first year as =
(74514/1.0609) = 70,236.63
The size of the loan will be around 70,236.63 for the same to be repaid within the two year of
frame time.

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References
Eisenberg, J., & Mishura, Y. (2018). An Exponential Cox-Ingersoll-Ross Process as Discounting
Factor. arXiv preprint arXiv:1808.10355.
Xiong, J., Zhang, Q., Sun, G., Zhu, X., Liu, M., & Li, Z. (2016). An information fusion fault
diagnosis method based on dimensionless indicators with static discounting factor and
KNN. IEEE Sensors Journal, 16(7), 2060-2069.