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Solution to 1 (a)
IN order to solve the first part, we need to follow the following formula –
M
=
P
[
i
(1 +
i
)
n
] / [ (1 +
i
)
n
 1]
Where M is the monthly payment.
i
=
r
/12. The same formula can be expressed much
different way, but this one avoids using negative exponentials which confuse some
calculators.
Plan A
Plan B
loan
225,000
225,000
interest
7.80%
6%
monthly interest (i)
0.0065
0.005
no. of years
25
15
no. of months (n)
300
180
Now in the above table, the monthly interest rate is 0.0065 and 0.005 respectively. We
have converted the yearly rate in to the monthly rate because we need to calculate the
monthly payments required under the two arrangements. This has been indicated as (i)
in the formula. This has been calculated by simply dividing the interest rate by 12.
These have been explained as follows: 7.8%/12 = 0.0065 and 6%/12 = 0.005
Now the number of years in this case is 25 years and 15 years and the periods
according to the formula has also been converted to the number of months. This has
been done by multiplying the no. of respective years with 12. These numbers are
explained as follows: 25 x 12 = 300 months and 15 x 12 = 180 months.
Now we can put all the values in the above mentioned formula as:
Plan A:
M = 225000x[0.0065x(1+0.0065)^300] / [(1+0.0065)^300 – 1]
Now, the most typical part of this equation is (1.0065)^300 which can be solved by
any scientific or financial calculator. The other options are using the logarithmic
functions. I HAVE STILL NOT USED THE MSEXCEL AS YOU HAVE
DICTATED BUT I HOPE THAT I HAVE THE LIBERTY TO USE THE
CALCULATORS. Using the calculator, the value of 1.0065^300 is 6.984475003.
solving the same, we get the value of M = $1706.88
Plan B:
M = 225000x[0.005x(1+0.005)^180] / [(1+0.005)^180 – 1]
Now, the most typical part of this equation is (1.005)^180 which can be solved by any
scientific or financial calculator. The other options are using the logarithmic
functions. I HAVE STILL NOT USED THE MSEXCEL AS YOU HAVE
DICTATED BUT I HOPE THAT I HAVE THE LIBERTY TO USE THE
CALCULATORS. Using the calculator, the value of 1.005^180 is 2.454093562.
solving the same, we get the value of M = $1898.68
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View Full DocumentSolution to 1 (b)
In order to get the status of the loan outstanding after 5 years, we will have to prepare
the amortization schedule.
Plan A:
Month
Beginning Bal.
Instalment
Interest
Principal
Ending Balance
1
225,000.00
1,706.88
1,462.50
244.38
224,755.62
2
224,755.62
1,706.88
1,460.91
245.97
224,509.65
3
224,509.65
1,706.88
1,459.31
247.57
224,262.08
4
224,262.08
1,706.88
1,457.70
249.18
224,012.90
5
224,012.90
1,706.88
1,456.08
250.80
223,762.10
6
223,762.10
1,706.88
1,454.45
252.43
223,509.67
7
223,509.67
1,706.88
1,452.81
254.07
223,255.60
8
223,255.60
1,706.88
1,451.16
255.72
222,999.88
9
222,999.88
1,706.88
1,449.50
257.38
222,742.50
10
222,742.50
1,706.88
1,447.83
259.06
222,483.44
11
222,483.44
1,706.88
1,446.14
260.74
222,222.70
12
222,222.70
1,706.88
1,444.45
262.43
221,960.27
13
221,960.27
1,706.88
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 Spring '10
 Ravikant

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