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# Fundamental of Finance

Time Value of Money

Fundamental of Finance: Time Value of Money: Annuity Cash Flows

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.

TIME VALUE OF MONEY 2
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
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.

TIME VALUE OF MONEY 3
At eight percent interest:
A=P( 1 + 1/r)^n
Where;
P = \$500
r = 8%
n = 5
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

TIME VALUE OF MONEY 4
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, \$665.51.331 = \$885.115 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, \$805.255*1.61051 = \$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 = \$1,024.87*0.909 = \$931.61

TIME VALUE OF MONEY 5
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= 770.00*0.683 = \$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.

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

TIME VALUE OF MONEY 6
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%
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 7

Reference

Cornett, M., Adair, T., & Nofsinger, J. (2013).M:Finance.McGraw-Hill/Irwin; 2 edition