Comprehensive Analysis of Time Value of Money Concepts and Problems

This assignment solution focuses on the core concepts of the time value of money, providing detailed calculations and explanations for various financial scenarios. It includes the computation of effective interest rates for different compounding periods, determining the future value of investments and deposits, and analyzing loan options to identify the most advantageous terms. The assignment also explores present value calculations for future cash flows and calculates equated annual installments for loans. Furthermore, it delves into the future value of annuities, comparing annual and semi-annual compounding. The solution uses formulas and step-by-step calculations to illustrate the concepts, accompanied by a bibliography of relevant academic sources, making it a comprehensive resource for finance students.

Running head: TIME VALUE OF MONEY
Time value of money
Name of the student:
Name of the University:
Authors Note:

1TIME VALUE OF MONEY
Answer to Question 1
The formula that is used for calculating the effective interest rate is given below:
Effective interest rate= (1+r/m)m -1
R is the rate of interest.
M is the number of times per year.
Statement showing calculation of effective interest rate
Account
Annual
Interest Rate
(R )
Compounded
period Times Per
Year (M)
Effective
Interest rate
A 10% Annually 1 10%
B 12% Monthly 12 13%
C 12% Bimester 6 13%
D 8% Quarterly 4 8%
E 10% Semi-annually 2 10%
F 12% Quarterly 4 13%
The future value of the money is calculated using the formula:
FV= Present value (1+rate of interest)^number of times
Statement showing calculation of compounded amount
Account
Amount
Deposited
(EUROS)
Annual
Interest Rate
(R ) Deposit
period
Number of
payment
period Compounded
Amount
A 1,000 10% 10 10 $2,593.74
B 95,000 12% 1 12 $370,117.72
C 8,000 12% 2 12 $31,167.81
D 120,000 8% 2 8 $222,111.63
E 30,000 10% 4 8 $64,307.66
F 15,000 12% 3 12 $58,439.64

2TIME VALUE OF MONEY
Answer to Question 2
Two banks are providing loan the bank that will provide loan at minimum interest should
be selected. Therefore, in order to make the decision effective interest rate are calculated below.
Statement showing calculation of effective interest rate
Particulars Finance company Bank
Rate of interest 12% 13%
Compounding 12 1
Effective interest rate 13% 13%
The effective rate of interest for both the loan is 13%. Therefore, it can be said that any
one of the option can be selected.
Answer to Question 3
Time year Amount Received (Euros) Present value
11 10000 $5,267.88
12 10000 $4,969.69
13 10000 $4,688.39
14 10000 $4,423.01
15 30000 $15,803.63
Amount that is deposited $35,152.59
The total amount that is required to be deposited today is $35152.59.
Answer to Question 4
The formula for calculating the annual loan payment is:
Annual payment= (r(P))/ (1-(1+r)-n)

3TIME VALUE OF MONEY
Calculation of equated Annual Installment
Particulars Amount (Euros)
Loan Amount 25000
Interest rate 12%
Time period 5
Equated Annual Installment 6935.24
Answer to Question 5
Statement showing future value of an annuity
Particulars Compounded Annually Compounded semi annually
Annuity amount 1000 1000
Time 10 10
Number of period 10 20
rate 10% 10%
Future value of Annuity $15,937.42 $57,275.00

4TIME VALUE OF MONEY
Bibliography
Kashyap, Ankita. "Capital Allocating Decisions: Time Value of Money." Asian Journal of
Management 5.1 (2014): 106-110.
Mpakaniye, Jean Paul. "Time Value of Money." (2014).