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Question 1134809: Angela wants to buy a house for 700000.she has a deposit of 50000 and take out a loan for the balance at a rate of 18% p.a compounded monthly
1.how much money must Angela
borrow from the bank?
2.calculate the monthly payment if she wishes to settle the loan in 15 years
3.Angela later won the lottery and wishes to settle the loan after the 50th payment.what is the outstanding balance?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! the house costs 700,000 and she has a deposit of 50,000.
the interest rate on the loan is 18% compounded monthly.
she puts her 50,000 down and she needs to borrow the remainder from the bank.
that remainder is equal to 700,000 - 50,000 = 650,000.
you can use a financial calculator to determine the monthly paymentw.
the one i use is the TI-BA-II.
using this calculator, i provide the following inputs.
present value is equal to 650,000.
percent interest rate per month is equal to 18/12 = 1.5.
number of months is equal to 15 * 12 = 180.
future value is equal to 0.
payments are made at the end of each month.
i then have the calculator tell me that the monthly payments are 10,467.736767 dollars payable at the end of each month, which would be rounded to 10,467.74 dollars.
if i want to know the remaining balance at the end of the 50th month, the financial calculator has the capability to tell me that directly, or i can figure it out by doing the following.
since there are 180 months in the loan, then after the 50th month, i have 180 - 50 = 130 months of payments left.
i use the calculator again and input the following.
present value = 0
future value = 0
number of months = 130
percent interest rate per month = 1.5
payment at the end of each month is equal to 10,467.73676.
i then have the calculator tell me that the present value of that loan is equal to 597,115.126 dollars.
that's the remaining balance after 50 months which is what i would have to pay to settle the loan.
there is a manual formula i can use to calculate the same thing.
that formula is shown below.
the first formula i would use is:
ANNUITY FOR A PRESENT AMOUNT WITH END OF TIME PERIOD PAYMENTS
a = (p*r)/(1-(1/(1+r)^n))
a is the annuity.
p is the present amount.
r is the interest rate per time period.
n is the number of time periods.
the inputs to this formula would be:
p = 650,000 (without the comma)
r = .18 / 12 = .015 (this is the rate, not the percent)
n = 12 * 15 = 180
the formula would become:
a = (650000*.015)/(1-(1/(1+.015)^180)).
the result from executing this formula in my calculator would be 10,467.74676.
this compares favorably with what the calculator told me.
the second formula i would use is:
PRESENT VALUE OF AN ANNUITY WITH END OF TIME PERIOD PAYMENTS
p = (a*(1-1/(1+r)^n))/r
p is the present value of the annuity.
a is the annuity.
r is the interest rate per time period.
n is the number of time periods.
the inputs to this formula would be:
a = 10,467.73676
r = .015
n= 180 - 50 = 130
the formula would then look like this:
p = (10,467.73676*(1-1/(1+.015)^130))/.015
i would enter it into my calculator exactly as shown.
it would then tell me that the present value is equal to 597,115.1262.
this compares favorably with what the financial calculator told me.
i can also do the calculations in excel and show you the month by month breakdown of the payments and the remaining in each time payment.
this provides a reasonable confirmation that the calculations were done correctly.
this is what the excel printout looks like.
i skipped non-essential months since they weren't necessary for you to understand what i was trying to show you.
the formula used in excel to calculate the monthly payments was:
=PMT(0.18/12,15*12,-F3)
.18/12 was the rate per month.
15*12 was the number of months.
-F3 was the negative value of the contents that were in cell F3.
finally, there is a function in the TI-BA-II that allows you to find the remaining balance at the end of the 50th month directly.
using this method, i was able to confirm that my other calculations were correct.
if you don't have a financial calculator handy, there is an online calculator you can use.
that calculator can be found at https://arachnoid.com/finance/
you should be able to duplicate my findings using this calculator, give or take a few pennies because of rounding.
if you are having trouble duplicating these answers, let me know and i'll guide you through it in more detail.
the tutorial where i got the manual formulas from can be found here:
https://www.algebra.com/algebra/homework/Finance/THEO-2016-04-29.lesson#f9
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