annually after which it will increase to 6% annually.
a)
Calculate the monthly installment for the first 2 years.
Ordinary Annuity

C=?; where PVA = 400 000; k=0.05/12: n=20*12=240
C=$2639.82
b)
Calculate the loan balance owing, at the end of the 2
nd
year.
PVA=? Where k=0.05/12; n=240-24=216
PVA=$375 489.74
c)
Calculate monthly installments after 2 years.
C=?; where PVA = 375 489.74; k=0.06/12: n=216
C=$2846.82
d)
Calculate the difference in monthly payment from a change in interest rate from 5% to 6%.
Increase in installment is $2846.82-$2639.82
=
$207
e)
If the installment remained unchanged, how much longer would it take to pay back the loan?
PVA =375489.74; c=$2639.82: k=0.06/12 using ordinary annuity formula:
375489.74 = 2639.82[(1-(1+0.06/12
)
-n
)/ 0.06/12]
142.24 = [(1-(1.005
)
-n
)/ 0.06/12]
0.7112 = 1-(1.005
)
-n
)
0.2888 = 1.005
-n
ln
0.2888/ln 1.005 = -n
-249.02 = -n
249.02 = n
So additional months is:
249-216 =
33 months approx.
3.
Construct an amortization schedule of a loan of $10,000 to be repaid over 10 years with a 10-
ordinary annuity payment at effective rate of interest of 10% per year.
Where PVA = 10000; k=0.10; n= 10
C= 1627.45
Year
Installment
Int. Pmt
Prin.
Pmt
Outstanding
balance
0
10000
1
1627.45
1000.00
627.45
9372.55
2
1627.45
937.26
690.20
8682.36
3
1627.45
868.24
759.21
7923.14
4
1627.45
792.31
835.14
7088.00
5
1627.45
708.80
918.65
6169.36
6
1627.45
616.94
1010.51
5158.84
7
1627.45
515.88
1111.57
4047.27

8
1627.45
404.73
1222.72
2824.55
9
1627.45
282.46
1344.99
1479.56
10
1627.45
147.96
1479.49
0.06
Note:
Interest is calculated on previous years balance at 10%
Principal pmt = installment –interest
Outstanding balance = previous years outstanding balance – current years principal payment
4.
Construct a sinking fund schedule for the loan of $15,000 to be repaid over 5 years with a
10-
ordinary annuity payment
at effective rate of interest of 8% per year.
Where FVA = 15000; k=0.08/2; n= 10
C=
1249.36
(sinking
fund
deposit)X
Year
Installment
Int. Pmt
Sinking Fund deposit
Sinking Fund
int.
Sinking Fund
bal.
0
1
1849.36
600
1249.36
0.00
1249.36
2
1849.36
600
1249.36
49.97
2548.69
3
1849.36
600
1249.36
101.95
3900.00
4
1849.36
600
1249.36
156.00
5305.36
5
1849.36
600
1249.36
212.21
6766.94
6
1849.36
600
1249.36
270.68
8286.97
7
1849.36
600
1249.36
331.48
9867.81
8
1849.36
600
1249.36
394.71
11511.89
9
1849.36
600
1249.36
460.48
13221.72
10
1849.36
600
1249.36
528.87
14999.95
Note:
Interest = 15000 x 0.08/2 =600 for each period as loan balance is same for all
Installment = interest + sinking fund deposit
Sinking fund int. = previous years sinking fund balance x 0.08/2
Sinking fund bal = previous years sinking fund balance + fund int. for this yr + sinking fund
deposit for this yr
THE END

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- Fall '19
- Interest, Mortgage loan, Jill