2. Kate will purchase a house for $500,000 with a 10% down payment and $10,000 i
ID: 2506951 • Letter: 2
Question
2. Kate will purchase a house for $500,000 with a 10% down payment and $10,000 in closing costs. The closing costs are included in the loan. A 10-year loan is arranged at 5% interest compounded monthly.
(a) What is the monthly payment?
(b) By choosing to include the closing costs in the loan, how much money was paid in interest on the closing costs over the life of the loan.
(c) What is the effective interest rate for this loan? (Hint: you must take into account the monthly compounding AND the closing costs.)
(d) Suppose closing costs were paid at closing. How does this change the overall cost of the loan? How does this change the effective interest rate?
(NOTE: EVERYTHING SHOULD BE DONE IN EXCEL. OTHERWISE NO POINTS. INCLUDE THE FUNCTION USED AS WELL. IF ITS POSSIBLE INCLUDE THE SPREADSHEET FILE AS WELL)
Explanation / Answer
down payment =50000
closing cost=10000 which will be added to total amount
hence amount is 500000-50000+10000 =460000
interest is compounded monthly and let p be monthly instalment
monthly rate is 5/12 =0.4166% =0.004167
number of months =12*10 =120
hence 460000 =p*(1/(1.004167) +1/(1.004167)^2 +1/(1.004167)^3 +....+1/(1.004167)^120)
hence 460000 =p*((1/(1.004167))^30 -1)/ (0.004167)
monthly payment p =14426.77
.......................
closing loan will be 10000 hence amount to be paid for closing loan =10000*(1+0.004167)^120 =16470
hence interest paid on closing =16470-10000 =6470
.....................
amount paid =monthly instalment *no of instalments =14426.77*120 =1731212.4
hence interest =1731212.4-460000 =1271212.4
interest =pnr/100
1271212 =460000*10*r/100
r =27.635 percent
...................
if closing cost are paid at the end and not included in loan
then
ence amount is 500000-50000 =450000
interest is compounded monthly and let p be monthly instalment
monthly rate is 5/12 =0.4166% =0.004167
number of months =12*10 =120
hence 450000 =p*(1/(1.004167) +1/(1.004167)^2 +1/(1.004167)^3 +....+1/(1.004167)^120)
hence 450000 =p*((1/(1.004167))^30 -1)/ (0.004167)
monthly payment p =14113.14
.......
amount paid =monthly instalment *no of instalments =14113.14*120 =1693577.35
hence interest =1693577.35-450000 =1243577.35
interest =pnr/100
1243577.35 =460000*10*r/100
r =27.034 percent
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