MSE304ClassProject-Part2 (1)

MSE 304- Part 1ETHAN BANTONMUBASHIR MAHMOODHAMDI AHMEDGERMAN ZEPEDAGYAN UPPAL

The Smithson's Project

Table of Contents

Page #

1. Introduction 3

2. Assumptions 4

3. Mortgage Plans 5-6

4. Calculations 7-10

5. Data 11-18

6. Conclusion 19-20

7. Questions 21

Introduction

After accumulating a down payment for a house, Paul and Leslie Smithson

have finally decided to take the plunge and buy their first home. After finally

deciding on a house that fits their needs, they have come to consult us regarding

the financial aspect of their house. We are given four different loan options to

review and analyze with the intentions of finding a mortgage that would maximize

the Smithson’s retirement account balance after 35 years or minimize the total

amount of paid interest over the course of the loan. With our goal to help the

Smithson’s make the safest and smartest choice, we began the analysis of the four

different loan options and will be making suggestions to them based on our results.

The cost of the house is $103,000 and the Smithson’s have accumulated

$10,000 to be used for the down payment and the closing cost of their home. Any

excess of the $10,000 will be used to make the initial deposit into their retirement

savings account. Their set budget is $1,000/month which should cover the

mortgage, any excess amount from the $1,000 would then be deposited into the

savings account. Furthermore, the yearly tax savings on the interest paid from the

mortgage will be invested into the retirement account as well.

Assumptions

1. The rate of the mortgages remains fixed over the years and value of $1,000

each month remains the same.

2. Paul and Leslie do not get a divorce over the course of buying their house

and remain a happy couple.

3. Paul and Leslie maintain steady jobs so that their income always remains

fixed and no extra charges are created.

4. The years remain at 52 weeks and the addition of leap year does not throw

off the payment cycle.

5. The amount of weeks in a month can be averaged out as a number that will

remain constant as the years progress.

Mortgage Plans

The first mortgage that is being offered to them has a 30 year fixed rate with

a given interest rate of 7.58% per year compounded monthly. This mortgages

monthly payments can be evaluated in two options. Either the entire $10,000 can

be used as a down payment or a minimum of 5% of the house cost can be used for

the down payment. If the entire $10,000 is paid, the left over loan amount is

$93,000, which gives us 93000+0.01*x x = 93000/0.99 = $93939.39. In this

case, there is no initial investment in the retirement account. In the second case,

however, there is an initial deposit in the retirement account. There is a minimum

5% down payment which comes out to $5,150. This mortgage option also includes

a 1-point closing cost which comes out of the $10,000 down payment. The total

amount for the closing cost is 1% of the loan value ($103,000-$5,150=$97,850)

which is $978.50. The remaining $3,871.50 goes directly into the retirement

account.

The second mortgage being offered now has a 15 year fixed rate instead of

the 30. The interest rate is 7.13% per year and it is compounded monthly. This

option also has monthly payments. Similar to the first mortgage, this mortgage also

the option of either paying the entire $10,000 for down payment or the minimum

5%. It also has a 1-point closing cost. If the entire $10,000 is paid as the down

payment, the loan payment comes out to $93,000. After including the 1-point

closing cost, the total loan payment is $93,930 which is similar to the first

mortgage. There will be no initial deposits in the retirement account in this case.

However, if the 5% minimum down payment of $5,150 is paid, there will be an

initial deposit in the retirement account ($3871.50) which is similar to the first

mortgage.

Unlike the first two options, the third option has bi-weekly payments. It has

a 30 year fixed rate with an annual interest rate of 7.08% compounded bi-weekly.

Similar to the first two mortgages, this mortgage also has two different options.

The first one being $10,000 as the down payment or the minimum 5% down

payment. The amounts are similar to the first and second mortgages as shown

above.

The fourth and final option is similar to the third option in the sense that it

has bi-weekly payments and the interest rate of 6.63% per year is compounded bi-

weekly as well. The cases for the down payments, however, are the same. So,

doing the calculations, we get the same numbers for the down payment

calculations as the first three options.

After doing the calculations for all four options listed above, we found out

that option three would be our suggested option for the Smithson’s as it would put

the most amount of money in their retirement account. The data shown below

proves our suggestion.

Calculations

The process of how we obtained our results were done through a series of

calculations. Values were obtained with both hand calculations through the

principles learned in class, as well as through the usage of Microsoft Excel

functions. Of the four mortgages, there were various factors that differed between

each option, however the process of our calculations were roughly the same. For

instance, with Mortgage 1, we took the down payment and its correlating loan

values into consideration, along with the 1-point closing cost. At a down payment

value of $10,000 and closing cost value of 1% of our loan value, we have

calculated a total loan value of $93,930. We repeated this step for the minimum

5% down payment which was calculated as $5150, leaving our loan value at

$97850. Next, we calculated our monthly interest rate from our fixed rate of 7.58%

per year, by dividing it by the total number of months giving a monthly interest

rate around 0.6317%. Next, we calculated the monthly payments. Knowing that

our present value is $93,930 we multiply it by the “A given P” (A/P) factor at the

rate of the monthly interest rate for the total amount of months in the period, which

for 30 years is 360 months. This value for the monthly payment yielded $661.93,

which we then confirmed using the PMT Excel function. Now that we have

calculated our monthly payment we obtain the amount invested towards the

retirement fund by subtracting the monthly payment to the Smithson’s budget of

$1000 giving us a value of $338.07. Our value for the interest is then calculated

using the IPMT function and the annual interest paid is found by compiling the

amounts every 12 payments. From this value we are able to obtain the principal

amount by calculated the difference between the payment amount and interest

amount for every month.

Now that we have finished those calculations we can take a further look at

the retirement fund. For the retirement, we want to calculate the effective interest

rate formula which essentially divides our nominal interest rate by the

compounding period. Since the Smithson’s earn such generous salaries they are

placed in the 28% effective income tax bracket for their personal income tax. With

this in mind, we have the ability of calculating the amount of tax refund they

receive at the end of every year by multiplying 0.28 to the amount of interest paid

every year. After summing up all the tax refunds per year we found that the total

amount refunded was $40,520.85 throughout the 30-year period. Knowing this

amount and how much tax is refunded individually each year, we calculated the

future value of the retirement savings every year using the effective interest rate for

the retirement, the amount of years left (n-1), and the refunded tax amount. After

calculating this for every year in the 30-year period we obtain a value of

$386,061.47. Next we must find the future value of the annual payments. This is

calculated by using the effective tax rate of the retirement fund in years, the

amount of months in the period (360), and the monthly investment towards the

savings account throughout the 30-year time period. We then calculated the future

value of the annual payments over 35-year period, as well as the future value of the

$1000 in the last five years after the Smithson’s have completed paying off their

mortgage. The future value of the 35 years is calculated by applying the effective

interest rate of the retirement fund to the future value of the annual payments over

the 30-year period for a duration of 5 years. Then for the last five years’ future

value is calculated by the full $1000 budget applied to the effective tax rate of the

retirement fund over those 60 months (5 years), which gives us a value of

$76,182.57. Finally, we are able to find the total retirement value by summing the

$386,061.47 and the $76,182.57 values with the future value of the annual

payments over the 35-year period yielding a total retirement value of

$1,511,664.79.

This whole process of calculations is then replicated for the minimum of 5%

down payment for every mortgage option listed. Instead of using the $10,000 value

for the down payment you will being using the calculated $5150, which is 5% the

total cost of the Tudor house. As a result, your loan value will increase by the

difference in down payments from the last example, however the overall process

from here will remain the same. Mortgage #2 is relatively similar, however in this

option you will be adjusting those calculations for 15-year period with a fixed

interest rate of 7.13% per year. Now this is not the same for Mortgage #3 and

Mortgage #4, since these options are created for bi-weekly payments rather than

monthly payments there are a few more components we must account for. The

time period and interest rates also shall be readjusted for each option and case, but

that’s not quite it. The main discrepancy is the conversion of the interest rate,

which is calculated for the monthly nominal interest rate along with the monthly

effective interest rate. This is done by converting the amount of bi-weekly

payments to monthly payments, which we calculated to be approximately a value

of 2.17. As for the rest, we apply the same process of computations.

Data

For Mortgage 1A ($10,000 down)

Interest rate /year/month 7.68%

Total Interest Paid $144,716.0774

Monthly Interest Rate .00631667%

Down payment $10,000

Total number of periods 360

Loan value $93,930

Monthly Payment $661.83

Monthly investment for Retirement $338.07

Total tax refund $40,520.85

Future total tax refund 35 years $386,061.47

Effective Interest Rate for retirement/year .093806

Effective interest Rate for retirement/monthly .007817241

Future annual payment for 30 years $670,264.71

Future annual payment for 35 years $1,049,420.74

Future $1,000 for years 30-35 $76,182.57

Total Retirement Value $1,511,664.79

For Mortgage 1B (5% down)




Down payment $5,150


Loan value $97,850

Remaining cash from down payment $3,871.50









Future remaining down payment 35 years $89,289.89

Future $1,000 for years 30-35 $76,182.57








Loan value $93,930









Future $1,000 for years 15-35 $701,115.95






Down payment $5,150


Loan value $97,850











Future $1,000 for years 15-35 $701,115.95



Interest rate /year/2-week 7.08%



Effective Interest Rate .005908702



Loan value $93,930









Future $1,000 for years 30-35 $76,182.57







Down payment $5,150


Loan value $97,850











Future $1,000 for years 30-35 $76,182.57









Loan value $93,930

Monthly Payment $825,43








Future $1,000 for years 15-35 $701,115.95







Down payment $5,150


Loan value $97,850











Future $1,000 for years 15-35 $701,115.95


Conclusion

After vigorous analysis, we were able to professionally suggest mortgage

three as the best mortgage plan for the Smithson family to maximize their

retirement account balance after 35 years. Numerical data calculated both by hand

and using digital technological services such as Microsoft Excel were required in

making an educated suggestion. These calculations were able to give us the

required monthly payment values and the amount of money that would be

available to put into a retirement fund. We had to take into account vital

differences in the mortgage values such as differences in payment periods, and

differences in the number of years for the mortgage plans. Mortgages required to

be paid over 30 years included mortgage options one and three, while mortgages

required to be paid over 15 years included mortgage options two and four.

Mortgages one and two, were to be paid monthly, while mortgages three and four

were paid bi-weekly. Taking these parameters into account, we calculated the

retirement values for each of the four mortgages. Mortgage 1 had monthly

payments of $689.55 and a retirement value of $1,530,954.62. Mortgage 2 had

monthly payments of $886.63 and a retirement value of $1,303,954.62. Mortgage 3

had monthly payments of $656.96 and a retirement value of $1,603,007.42.

Mortgage 4 had monthly payments of $859.88 and a retirement value of

$1,347,794.74. It is apparent that mortgage three which has the minimum down

payment ended up having the lowest monthly payments, and the highest retirement

value out of all of the mortgages. In the case of determining a mortgage to

minimize the total interest paid over the loan, Mortgage 4 with the maximum down

payment option kept the interest payment lowest of all the given options. After

presenting our data to the Smithson family we hope they chose the option that best

suits their needs.

Questions

1.) For mortgages 3 and 4, would the values of the retirement and monthly

payments be different if we did the values in accordance to biweekly calculations

instead of moving everything to monthly? Would we have paid less interest or

would the values be identical?

2.) It seems that for the 15 year loans, there is less of a value in the retirement fund

but lower interest is paid on the loan. Is there a benefit in paying over longer

periods of time or is that just because we are factoring in a retirement account that

it's more beneficial to pay of a long time period?

3.) If the retirement plan was compounded quarterly or semi-annually, would that

affect the value at the end? Would the amount in the retirement plan be higher or

lower?

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MSE304ClassProject-Part2 (1)