# Quantitative Methods - Assignment Example

Summary
The first type, the repayment Mortgage can be paid by a series of regular payments or instalments. Its value is equal to the present value of all future instalments. An example of this mortgage is a mortgage taken on a property.
If an Interest Only Mortgage is taken out then only the interest is paid over the mortgage period…

## Extract of sample"Quantitative Methods"

Download file to see previous pages For calculating the monthly expenses for the both types of mortgages first the nominal interest rates should be used to calculate the effective annual interest rates. This is done by using the following formula: I=(1+r/x)^x-1
In order to obtain the effective annual rates the Microsoft Excel formula was used: EFFECT(nominal_rate,npery), where nominal_rate is the annual nominal rate and npery is the number of compounding times per year.
These values were calculated in Microsoft Excel using the formula: PMT(rate,nper,pv,fv,type). Rate is the interest rate of the mortgage, Nper is the total number of repayments for the loan, in this case 300 months (25*12), Pv is the present value of the total repayments that are to be made, Fv is the future value that one wishes to attain after the last repayment, in this case 0 and lastly Type indicates whether the repayment is made at the beginning of the month (0) or at the end (1), in this case we assume it is made at the start of the month so 0.
In order to evaluate the Interest Only Mortgage option we must first calculate the effective annual interest rate on the deposit placed in the sinking fund. This will be done in the same way as for the Repayment Mortgage. The results are presented in the table below:
The monthly cost Interest Only mortgage consists of the interest paid over the mortgage period and the amount accumulated in the sinking fund....
epayments for the loan, in this case 300 months (25*12), Pv is the present value of the total repayments that are to be made, Fv is the future value that one wishes to attain after the last repayment, in this case 0 and lastly Type indicates whether the repayment is made at the beginning of the month (0) or at the end (1), in this case we assume it is made at the start of the month so 0.

In order to evaluate the Interest Only Mortgage option we must first calculate the effective annual interest rate on the deposit placed in the sinking fund. This will be done in the same way as for the Repayment Mortgage. The results are presented in the table below:

Nominal interest rate on deposit in sinking fund
Number of compounding periods per year
Effective annual interest rate on deposit in sinking fund
5.50%
1
0.055
5.75%
1
0.0575
6.00%
1
0.06
6.25%
1
0.0625
6.50%
1
0.065
6.75%
1
0.0675
7.00%
1
0.07
7.25%
1
0.0725
7.50%
1
0.075
7.75%
1
0.0775
8.00%
1
0.08
8.25%
1
0.0825
8.50%
1
0.085
8.75%
1
0.0825
9.00%
1
0.09

The monthly cost Interest Only mortgage consists of the interest paid over the mortgage period and the amount accumulated in the sinking fund. In order to calculate the monthly payment into the sinking fund using Excel the PPMT(rate,per,nper,pv,fv,type) formula was used where rate is the interest rate per period, per is the period, nper is the total amount of payments in the sinking fund, pv is the present value of the mortgage, fv is the future value expected in our case 0 and type indicates when the monthly payments are due in this case we assume that they are made at the beginning of the period so we take the value 1. The results are listed below:

Annual interest rate
Number of years in the loan
Amount of loan
Payment into investment plan
5.50%
25
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