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Sun 10 Mar, 2013 12:00 pm
Who can help me with solving this question?
You are going to buy a restaurant. The purchase price is €500,000 and you will take a mortgage. The bank requires that you pay initially 20% of the purchase price, then the mortgage will cover the remaining amount. You can over make the initial payment from your savings. The balance will then be paid a period of 20 years, using monthly payments at an annual percentage rate (APR) of 9%.
The mortgage terms allow you to pay the remaining balance on the loan at any time, without any additional cost or penalty. You hope that the restaurant will be a great success and you will be able to pay the balance of the mortgage after 5 years (i.e, the first payment in year 6 will be the remaining balance of the loan).
How much do you expect to pay in the first month of year 6, in order to clear the balance?
My calculations so far:
Mortgage = 400,000
Initially payment = 100,000
effective annual interest rate on your loan = [1+(r/m)^m]^t
r= 0,09
m=12 (monthly)
t=20 years
Gives [1+(0,09/12)^12]^20 = 6,009151524
@kuyt1,
kuyt1 wrote:
My calculations so far:
Mortgage = 400,000
Initially payment = 100,000
effective annual interest rate on your loan = [1+(r/m)^m]^t
r= 0,09
m=12 (monthly)
t=20 years
That equation for "effective annual interest" is not correct. The formula you want is the payment formula.
BAL/PMT = [ 1 - (1 + r/m) ^ (-t*m)] / (r/m) = [ 1-.0075]^240 / .0075 = 21.9
PMT = 3,599
To find the amount you will owe with 15 years left, use the same formula but put in the known payment and time period (15 years instead of twenty) and solve for the balance.
BAL = 3599 * [1-(1+.0075)^(-180)]/.0075 = 354,828.20
@engineer,
How did you go from BAL/PMT= [ 1 - (1 + r/m) ^ (-t*m)] / (r/m) to [ 1-.0075]^240 / .0075 = 21.9??
If i fill in the formula i get: [ 1- (1+.0075)^-240] / .0075] = 111.14
For the PMT calculation:
PMT = 400,000 * (0.0075) / (1-(1+0.0075)^(-240)) = 3599
So i expect to pay 354,828.20 in the first moth of year 6, in order to clear the balance? (correct awnser?)
@kuyt1,
The 21.9 is incorrect. (I originally was going to use a different formula then edited it. Glad to see you were working through it yourself.)
Yes, the answer is as listed. Note that I get that number through a calculator that was not rounding any values like 3599. If you round in some of the previous steps you will get something a few dollars off from the number listed.
@engineer,
Thanks.
Maybe you can help me with another question i posted on this forum?
http://able2know.org/topic/210218-1
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