Time Value of Money
Your opinions can make a difference! Are you satisfied with the way your college is run? Complaining
about a situation is easy to do. But developing & implementing solutions require much greater effort. Take
time to scrutinize possible campus issues. Then choose the issue to address in your letter. The following
ideas may spark your imagination and help with your selection: Is the campus ignoring cultural diversity or
other lifestyle issues? Does the parking lot need repairs, & security? Are you satisfied with the quality of
professors or the curriculum needs in your college? Does the bookstore charge exorbitant prices? �
Writing Hints: Address your letter to the appropriate person. Use exact title, accurate address, & correct
names Carefully consider the audience for your letter and be mindful of your tone. Avoid being angry.
Remember that more than your addressee may read your letter Use the AIDA approach in your letter for
your message to be persuasive to your reader.
TIME VALUE OF MONEY 2
Time Value of Money
Q1. I would rather have a savings account that paid interest compounded on an annual basis
(Cornett, Adair, & Nofsinger, 2013). The reason for this is because for the monthly basis the
interest is more likely to be higher than that of an annual basis.
Q 2. An amortization schedule is a detailed table showing regular payments that an individual
pays over time for a mortgage. It is used in determining the amount of an outstanding loan at
different times and adjusting the amount of loans so as to be in line with the expected monthly
payments.
Q3. The early years are more use full in reducing taxes than the late years since in settling the
loan during early years, and then it means that the time of the compounding factor is minimized.
Therefore the overall interest will be low as compared to when you could have paid it in the later
years.
Q4. The difference between an ordinary annuity and annuity due is in the difference between
their payment periods and time in relation to the period that is being covered by the payment. In
ordinary annuity, payments are made at the end of the covered period unlike in annuity where
payments are made at some regular intervals of time.
Q5.
Future value, A=P(1+1/r)^n
TIME VALUE OF MONEY 3
Where;
P = $500
r = 9%
n =5 years
1 st year= $500(1+0.09)^1 = $5451.09 = $594.1 2 nd year=$500(1+0.09)^2 = $594.051.188= $705.8
3 rd year=$500(1+0.09)^3 = $647.511.295 = $838.53 4 th year=$500(1+0.09)^4 = $705.81.411 = $995.9
5 th year=$500(1+0.09)^5= $769.312*1.5382 = $1183.4
Summing them up, ($594.1 + $705.8 + $838.53 + $995.9 + $1183.34 ), we will have $4317
Finding the average for the five years, ($4317/5) we get 863.537, and this is the future value of a
$500 annuity payment for the period of five years at an interest rate of nine percent.
At eight percent interest:
A=P( 1 + 1/r)^n
Where;
P = $500
r = 8%
n = 5
TIME VALUE OF MONEY 4
1 st year= $500(1+0.08)^1= $5401.08 = $583.2 2 nd year=$500(1+0.08)^2= $583.21.664 = $970.45
3 rd year=$500(1+0.08)^3= $629.91.25971 = $793.43 4 th year=$500(1+0.08)^4= $680.21.36049 = $925.5
5 th year=$500(1+0.08)^5= $734.66*1.46933= $1079.5
Summing them, ($583.2 + $970.45 +$793.43 + $925.5 + $1079.5) we will have $4352.04
Finding the average for the five years, ($4352.04/5), we get 870.41, and this is the future value of
a $500 annuity payment for the period of five years at an interest rate of eight percent.
At ten percent interest:
A=P( 1 + 1/r)^n
Where;
P = $500
r = 10%
n = 5 years
1 st year= $500( 1+0.1)^1= $550, $5501.1 = $605 2 nd year=$500( 1+0.1)^2= $605, $6051.21 = $732.05
3 rd year=$500( 1+0.1)^3= $665.5, $665.5*1.331 = $885.115
TIME VALUE OF MONEY 5
4 th year=$500( 1+0.1)^4= $732.05, $732.051.4641 = $1,071.79 5 th year=$500( 1+0.1)^5= $805.255, $805.2551.61051 = $1296.54
Summing them up, ( $605 + $ 732.05 + 885.115 + $1,071.79 + $1296.54 ) we get $4590.50.
Finding the average for the five years, ( $4590.50/5), we get $918.099, and this is the future
value of a $500 annuity payment for the period of five years at an interest rate of ten percent.
Q 6. A= P( 1+1/r)^n
Where;
P = $700
r = 10%
n = 4 years
1 st year= $700(1+0.1)^4 = $1,024.870.909 = $931.61 2 nd year= $700(1+0.1)^3 = $931.70.826 = $769.58
3 rd year= $700(1+0.1)^2 = $847.000.751 = $636.097 4 th year= $700(1+0.1)^1= 770.000.683 = $525.91
Summing them up, ($931.61 +$769.58 + $636.097 + $525.91) we will have $2863.197
Finding the average for the four years, ($2863.197/4) we get 715.8, and this is the present value
of a $700 annuity payment for the period of four years at an interest rate of ten percent.
TIME VALUE OF MONEY 6
At nine percent interest:
A=P( 1 + 1/r)^n
P = $700
r = 9%
n = 4 years
1 st year= $700(1+0.09)^4=$988.120.917=906.12 2 nd year=$700(1+0.09)^3=$906.520.842=763.3
3 rd year=$700(1+0.09)^2=$831.67=0.772=642.05
4 th year=$700(1+0.09)^1=763*0.7508=540.204
Summing them we will have, ( $906.12 + $763.3 + 642.05 + $540.204 ) = $2851.67
Finding the average for the four years ( $2851.67/4), we get 712.92, and this is the present value
of a $700 annuity payment for the period of four years at an interest rate of nine percent.
At eleven percent interest;
A=P( 1 + 1/r)^n
P = $700
r = 11%
TIME VALUE OF MONEY 7
n = 4 years
1 st year = $700(1+0.11)^4 = $1062.65, $1062.650.901= $957.45 2 nd year = $700(1+0.11)^3 = $957.34, $957.340.812 = $777.36
3 rd year = $700(1+0.11)^2 = $862.47, $862.470.731 = $630.47 4 th year = $700(1+0.11)^1 = $777, $7770.659 = $512.04
Summing them up we get, ( $957.45 + $777.36 + $630.47 + $512.04) = $2,877.323
Finding their average for the four years, ($2,877.323/4), we get $719.33075, and this is the
present value of a $700 annuity payment for the period of four years at an interest rate of eleven
percent.
TIME VALUE OF MONEY 8
Reference
Cornett, M., Adair, T., & Nofsinger, J. (2013).M:Finance.McGraw-Hill/Irwin; 2 edition
