Time Value of Money
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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
Where;
P = $500
r = 9%
n =5 years
1st year= $500(1+0.09)^1 = $545*1.09 = $594.1
2nd year=$500(1+0.09)^2 = $594.05*1.188= $705.8
3rd year=$500(1+0.09)^3 = $647.51*1.295 = $838.53
4th year=$500(1+0.09)^4 = $705.8*1.411 = $995.9
5th 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
1st year= $500(1+0.08)^1= $540*1.08 = $583.2
2nd year=$500(1+0.08)^2= $583.2*1.664 = $970.45
3rd year=$500(1+0.08)^3= $629.9*1.25971 = $793.43
4th year=$500(1+0.08)^4= $680.2*1.36049 = $925.5
5th 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
1st year= $500( 1+0.1)^1= $550, $550*1.1 = $605
2nd year=$500( 1+0.1)^2= $605, $605*1.21 = $732.05
3rd year=$500( 1+0.1)^3= $665.5, $665.5*1.331 = $885.115
4th year=$500( 1+0.1)^4= $732.05, $732.05*1.4641 = $1,071.79
5th 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
1st year= $700(1+0.1)^4 = $1,024.87*0.909 = $931.61
2nd year= $700(1+0.1)^3 = $931.7*0.826 = $769.58
3rd year= $700(1+0.1)^2 = $847.00*0.751 = $636.097
4th 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
1st year= $700(1+0.09)^4=$988.12*0.917=906.12
2nd year=$700(1+0.09)^3=$906.52*0.842=763.3
3rd year=$700(1+0.09)^2=$831.67=0.772=642.05
4th 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%
n = 4 years
1st year = $700(1+0.11)^4 = $1062.65, $1062.65*0.901= $957.45
2nd year = $700(1+0.11)^3 = $957.34, $957.34*0.812 = $777.36
3rd year = $700(1+0.11)^2 = $862.47, $862.47*0.731 = $630.47
4th year = $700(1+0.11)^1 = $777, $777*0.659 = $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
Reference
Cornett, M., Adair, T., & Nofsinger, J. (2013).M:Finance.McGraw-Hill/Irwin; 2 edition
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