The Time Value of Money

Issue A 

Money has a time value generally expressed as an interest. The right to one dollar today is more valuable than the right to one dollar one year from now, this is shown by the amount that could be earned by investing one dollar for one year. If interest is not repaid as it accumulates, the amount to be received increases at a compound rate reflecting the fact that, the interest received must be made available (MoneyHabits, 2018). Consequently, if this interest is unpaid, it should continue earning until it is paid. Interest is an amount of money which is paid to you when you make an investment or which you have to pay when you take out a loan ( MoneyHabits, 2018) . The compound interest is the interest calculated on the principal amount and also on the total accumulated interest. It is arrived at by multiplying the principal amount by one adding the annual interest rate raised to the number of compound periods subtracted one ( Financial Mentor, 2018). The initial total amount of the loan is then subtracted from the resulting value. The compound interest calculation in the case study of Mary is shown below; Formula;

P  = the principal amount. 

I  = rate of interest stated as a decimal 

n  = is the number of compounding periods per year. 

T = this is the time expressed in years. 

P  = 500, 

  i = 5 / 100 = 0.05,  

n = 19. 

Calculation 

= $16,533 

After 20 years, the total amount of money deposited by Mary will certainly have changed. The principal amount will have increased. And the Principal will become the amount currently in the account. If Mary chooses to close the account after making another deposit of $500, she will get an amount of $16,533 from the bank at the end of the last deposit and closing of the account. Taking into consideration the compound interest accumulated over the years, the interest amount cannot be the same (Jo, 2013). 

Issue B 

This is like an investment to Mary. Since the power of compounding enables Mary's money to grow exponentially over time. This is so because the returns from previous years remain invested. 

Total amount per year = $75,000. 

Period to be paid=20 yrs. 

Interest rate=7% 

Total amount to be earned after 19 years: 

=$2,803,422.37+ 75000 =$2,878,422.37 

This is the total amount of money to be paid by the university each year. So after 20 years, the total payout will add up to. 

$2,803,422.37 

+ 75,000.00 

$ 2,878,422.37- The total amount she stands to benefit. 

Since Mary wants to be paid the whole amount a once, we have to calculate the present value of an annuity. This is supposed to show the total amount that she is likely to receive after 20 years. The present value of an annuity is the sum of all payments made and the interest earned on an account ( Koening, 2011). 

Formula

i=interest rate (this is the amount charged and is expressed as a percentage of principal) 

FV=future value - this is the value of the amount or an asset at a specified date 

t = period 

n = number of times the interest is compounded per year 

Hence; 

The total future value to be paid to Mary is; 

= $743,839.039 

Therefore, if Mary wants to be paid the total amount at once, she is likely to receive a total of $743,839.039 . 

According to the calculations above, it is very crucial and critical to consider the necessity and importance of being paid in a one lump sum. 

Issue C 

The present value of annuity represents the promised future payments which have been discounted to an equivalent value right now (Koening, 2011). To come up with the present value of the deferred annuity, we can discount the previous figure using the given interest rate and the number of periods before the payments commence. We can achieve this by using the PV formula: PV [(1/(1+r))^t], PV stands for the amount at the start period when the payments begin, and t represents the number of periods at the time when no payments are made (Koening, 2011). But in this case we have already obtained the future value; we can easily obtain the present value using the future value and the period remaining after the three years. 

Working: 

The Present Value of Annuity is; 

Whereby 

FV=Future Value 

i=Interest Rate 

t = number of years the amount is deposited or borrowed for. 

n = number of times the interest is compounded per year 

Hence; 

Future Value is the total amount to be paid to Mary 

= $882,427 

Mary will receive a total of $ 882,427. This shows that the additional working period would increase the present value of her bonus. Present value calculations entail the  compounding of interest .  It implies that any interest earned is reinvested and will earn interest at the same rate as the  principal .  In other words, you gain "interest on interest." The compounding of interest can be very significant when the interest rate and/or the number of years are sizable ( Averkamp, 2018). 

Issue D 

If Mary has decided to pay half of the school fees, which is $5500, then the $5500 is the principal amount. The interest rate that is used is 4% and is compounded annually. The time for starting college is also shown as 10 =10 years. The school Fees is likely to increase by 7% per year. In Mary's case study this can be solved by calculating the present value of the annuity of each payment using the present value formula (Averkamp, 2018). We can then add up the results from every calculation. 

The calculation below shows the total fees that Mary will pay each year at Beth’s college. 

1 st year of college = =$39,343 

2 nd year of college= =$47,597 

3 rd year of college= =$56,428 

4 th year of college= =$65,879 

The total fees that Mary will contribute to Beth’s college education will be. 

$39, 343 + $47,597 + $56,428 + $65,879 = $209,247 

Since Mary wants to start making deposits yearly, every deposit she makes will cover will cover the fees she will contribute to Beth’s college fees. These deposits will then earn an interest of 4% each year for six years until Beth starts college. 

Calculation of the total amount 

Whereby; 

P  = principal amount 

I  = annual rate of interest 

n  = number of interest periods 

A  = amount of money accumulated after n years, including interest. 

From the case study we can tell that: P  =? i = 4 / 100 = 0.04, n = 6, A=$ 209, 247 

We are trying to find P which is the deposit amount to be made by Mary. 

209,247=6.67P 

P=$ 31,546.47 

The deposit amounts that Mary will have to make will be $31, 546.47 each year for six years in order to be able to pay part of Beth’s fees. 

Summary 

If someone receives money today, it is likely to grow over time. This is due to the aspect of time value of money. This shows that money of a certain figure is more valuable right now than a year from now (Jo, 2013). Like in the case study of Mary, she will get more money because money received twenty years from now has a smaller present value than the money she would have received right now. The case study also depicts that calculations of present value can help individuals to understand aspects like the amount of money they can invest now in return for a certain value of cash to be received in future. 

References 

Jo, M. (2013). Compounding vs amortizing interest-the Untold Story . Retrieved from http://fiscalbridge.com/compounding-vs-amortizing-interest-the-untold-story/ 

Averkamp, H. (2018). Present value of an ordinary annuity . Retrieved from https://www.accountingcoach.com/present-value-of-an-ordinary-annuity/explanation 

Financial Mentor. (2018). Compound interest calculator (Daily to Yearly) . Retrieved from https://financialmentor.com/calculator/compound-interest-calculator 

Koening, E. (2011). Present value calculations for a deferred annuity . Retrieved from https://www.sapling.com/8191251/present-value-calculations-deferred-annuity 

MoneyHabits. (2018). The different types of interest . Retrieved from http://www.moneyhabits.com/types_of_interest.htm