CAN YOU PLEASE SHOW ALL THE MATH STEPS. THANK YOU (10 points) Using the two link
ID: 1145888 • Letter: C
Question
CAN YOU PLEASE SHOW ALL THE MATH STEPS. THANK YOU
(10 points) Using the two links below, figure out the monthly payments on a $100,000, 30 year mortgage loan on April 1971 and compare to the monthly payment on May 2014. What is the relationship between the interest rate and the fixed monthly payment (be specific)? Hint, on the Bank Rate site, enter $100,000 as the mortgage amount, 30 years as the term in years, and the relevant interest rate (take to two decimal places), then click on calculate.
Bank Rate site:
http://www.bankrate.com/calculators/mortgages/mortgage-payment-calculator.aspx
30 mortgage rates:
http://research.stlouisfed.org/fred2/series/MORTG
(click on 'view data' on upper left of screen)
(5 points) What is the percent difference in monthly payments?
(5 points) Now compare the total interest payments using May 2014 vs. April 1971.
(5 points) Using an interest rate = 5%, compare the present value of $100,000 one year from now to the present value of $100,000 five years from now.
Explanation / Answer
In April 1971 the bank rate was 7.31%. So on the basis of Interest on 1971 we calculate the that the monthly payment is $686.25. Here we have taken 30 years as term in years. On the other hand the interest rate on May 2014 is 4.19%. On the basis of this interest rate fixed monthly payment is $488.43. Here also we have taken 30 years as term in years. So we are getting from here is that when interest rate is 7.31%(as on April 1971) the fixed monthly payment is high i.e $686.25 where as when the interest rate is low (as on May 2014) i.e $488.43. So we can summarily say that when interest rate or bank rate is high monthly payment is high and when interest rate or bank rate is low monthly payment is low. Therefore a direct or positive relation is there between interest or bank rate and fixed monthly payment.
On the basis of bank rate April 1971 the fixed monthly payment is $686.25 and on the basis of bank rate May 2014 fixed monthly payment is $488.43. So we can calculate In 688.25 the difference is (688.25 - 488.43) = 199.82, So percent difference in monthly payment is (199.82/688.25)*100 = 29.03%. This is the percentage decrease in monthly payment comparing between April 1971 to May 2014. If we want to calculate percentage increase it will be just (199.82/488.43)/*100 = 40.91% . So the monthly payment increased in May 2014 to April 1971 is 40.91%.
If we compare the total interest payment we get that on the basis of bank rate in April 1971 the total interest payment is $147051 , whereas on the basis of bank rate in May 2014 the total interest payment is $75837. So interest payment is high (147051) when the bank rate is high (7.31% , April 1971) and interest payment is low (488.43) when the bank rate is low (4.19%, May 2014). So here also positive realtion when bank rate high total interest payment is and when bank rate is low the total interest payment is low.
Now we have to calculate present value of $100,000 one year from now to the present vlue of 100,000 five years from now. Interest rate is 5%. If we want to calculate the present we need to calculate the discounting value on the basis of interest rate and number of years. Formula for discounting value present worth is (1+i)-n . Here i, is the interest rate i.e 5%. The number of years is 1 in first case and 5 in second case . For first one i = 5%=0.05 , n =1 , So discounting factor is (1+0.05)-1 = 0.9523 , So after 1 year with 5% interest the present value of 100,000 will be equal to 100,000 * 0.9523 = $95,238. Now we calculate the discounting value for i =0.05 and n=5 years , (1 +0.05)-5 = 0.7835 , So we get the present value 100,000 after 5 years with 5% interest rate is 100,000 * 0.7835 = $78,350. So, Present value after 1 year (95238) is more than the present value after 5 years from now ( 78,350).
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