Mathematics for Business and Finance: Solutions and Analysis

This document presents a comprehensive solution to a Mathematics for Business and Finance assignment. The assignment covers various financial calculations, including present and future value of money, compound interest, and annuities. The solutions demonstrate the application of formulas to solve problems related to periodic withdrawals, loan terms, and investment planning. The student addresses questions involving the calculation of present values, effective interest rates, and the number of periods required to reach specific financial goals. The document includes detailed steps, formulas, and explanations for each problem, providing a clear understanding of the financial concepts involved. The assignment covers topics such as calculating the term of a loan, determining the time required for an investment to grow to a certain amount, and analyzing the impact of different interest rates and compounding periods. Overall, the assignment provides a practical application of mathematical principles in a business and financial context.

Running head: MATHEMETICS FOR BUSINESS AND FINANCE
Mathematics for Business and Finance
Name of the Student:
Name of the University:
Author’s Note:

2MATHEMATICS FOR BUSINESS AND FINANCE
Table of Contents
Answer to question 1:......................................................................................................................3
Answer to question 2:......................................................................................................................4
Answer to question 3:......................................................................................................................5
Answer to question 4:......................................................................................................................6
Part a:...........................................................................................................................................7
Part b:...........................................................................................................................................7
Answer to question 5:......................................................................................................................8
Bibliography:.................................................................................................................................10

3MATHEMATICS FOR BUSINESS AND FINANCE
Answer to question 1:
Periodic withdrawals = $3,000 at the beginning of every 6 months
Present balance in the fund = $25,000
Interest rate = 6.36% compounded semi-annually
Applying the present value formula of annuity due,
25000=3000+3000×
[ 1−( 1+ 6.36 %
2 )
−(n ×2−1)
6.36 %
2 ]
25000−3000
3000× 1
0.0318
=1− (1.0318 )−(n × 2−1)
0.2332−1=− ( 1.0318 )−(n ×2−1)
0.7668= ( 1.0318 )−(n × 2−1)
Taking log in both the sides,
log 0.7668=−( n× 2−1)× log 1.0318
−0.11532=− ( n ×2−1 ) ×0.013596
n ×2= 0.11532
0.013596 +1
n ×2=9.482049

4MATHEMATICS FOR BUSINESS AND FINANCE
n= 9.42049
2
n=4.74
Therefore, after 5 withdrawals the fund will be depleted.
Answer to question 2:
Annual interest rate = 7.30%
Loan amount = $609,500
Monthly payment = $17,400
Effective annual interest rate = (1+ 7.30 %
2 )2
−1
12 =7.43 %
Applying the present value formula of annuity due,
609500=17400×
[ 1−( 1+ 7.43 %
12 )
−(n × 12)
7.43 %
12 ]
609500
17400× 1
0.006194
=1− ( 1.006194 ) −(n ×12)
0.21698−1=− ( 1.006194 )−(n ×12)
0.78302= (1.006194 )−(n× 12)
Taking log in both the sides,

5MATHEMATICS FOR BUSINESS AND FINANCE
log 0.78302=−(n ×12) ×log 1.006194
−0.10623=− ( n ×12 ) ×0.00268
n ×12=0.10623
0.00268
n ×12=39.61
n=39.61
12
n=3.30
Term of the loan is 3.30 years.
Answer to question 3:
Cost of the truck = $56,000
Down payment = $5,600
Mortgage amount = $56,000-$5,600 = $50,400
Interest rate = 7.5% compounded semi-annually
Effective annual interest rate = (1+ 7.50 %
2 )2
−1
12 =7.64 %
Monthly payment = $1,800
Applying the present value formula of annuity due,

6MATHEMATICS FOR BUSINESS AND FINANCE
50400=1800 ×
[ 1−( 1+ 7.64 %
12 )
−(n× 12)
7.64 %
12 ]
50400
1800× 1
0.006367
=1− ( 1.006367 )−(n × 12)
0.178281−1=− ( 1.006367 )−(n ×12)
0.821719= ( 1.006367 )−(n × 12)
Taking log in both the sides,
log 0.821719=−(n× 12) × log1.006367
−0.08528=− ( n ×12 ) ×0.002756
n ×12= 0.08528
0.002756
n ×12=30.94
n=30.94
12
n=2.58
Number of time required = 2 years and 6.94 months
Answer to question 4:
Future value required = $35,000

7MATHEMATICS FOR BUSINESS AND FINANCE
Monthly contribution = $2,100
Interest rate = 4.5% compounded monthly
Part a:
Applying the present value formula of annuity due,
35000=2100×
[ ( 1+ 4.5 %
12 )
( n × 12 )
−1
4.5 %
12 ]
35000
2100× 1
0.00375
= ( 1.00375 )(n× 12)−1
0.0625+1= ( 1.00375 )(n ×12)
1.0625= (1.00375 )(n ×12)
Taking log in both the sides,
log 1.0625=(n ×12)× log 1.00375
0.026329= ( n ×12 ) × 0.001626
n ×12=0.026329
0.001626
Number of payments = 16.20
Part b:
Applying the present value formula of annuity due,

8MATHEMATICS FOR BUSINESS AND FINANCE
35000=2100×
[ ( 1+ 4.5 %
12 )
( n × 12 )
−1
4.5 %
12 ]
35000
2100× 1
0.00375
= ( 1.00375 )(n× 12)−1
0.0625+1= ( 1.00375 )(n ×12)
1.0625= (1.00375 )(n ×12)
Taking log in both the sides,
log 1.0625=(n ×12)× log 1.00375
0.026329= ( n ×12 ) × 0.001626
n ×12=0.026329
0.001626
Time period required = 0.026329
0.001626 ×12 = 1.35 Years
Answer to question 5:
Future value = $12,000
Interest rate = 3.90% compounded monthly
Number of deposit = 33
Monthly payment = (A)

9MATHEMATICS FOR BUSINESS AND FINANCE
Applying the present value formula of annuity due,
12000= A ×
[ (1+ 3.9 %
12 )33
−1
3.9 %
12 ]
12000= A × [ ( 1.00325 ) 33−1
0.00325 ]
12000= A × [ 0.113019
0.00325 ]
A=12000
34.78 =345.07

10MATHEMATICS FOR BUSINESS AND FINANCE
Bibliography:
Banerjee, B., 2015. Fundamentals of financial management. PHI Learning Pvt. Ltd.
Flórez, M., Vera, M., Salazar-Torres, J., Huérfano, Y., Gelvez-Almeida, E., Valbuena, O., Vera,
M.I. and Aranguen, M., 2019, November. Interest rates calculation in certain ordinary annuities.
In Journal of Physics: Conference Series (Vol. 1414, No. 1, p. 012009). IOP Publishing.