Question 1140679: Angela wants to buy a house for R700000.She has a deposit of R50000 and takes 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 to settle the loan in 15 years.
(3) Angela later won the lottery and wished to settle the loan after the 50th payment.What is the outstanding balance?
Please help me I begg
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! the price of the house if 700,000
the deposit is 50,000
the mortgage is therefore 700,000 minus 50,000 = 650,000.
i used the texas instruments business analyst 2 (TI-BA-II).
inputs were:
present value = 650,000
future value = 0
interest rate = 18% per year / 12 = 1.5% per month.
number of months = 15 years * 12 = 180 months.
payments are made at the end of each month.
calculator says that the end of month payments need to be 10,467.73676.
after the 50th payment, there are 180 - 50 = 130 months left to pay.
to find out what the remaining balance is after the 50th payment, you need to find the present value of the payments for 130 months.
inputs to the calculator would be:
present value = 0
future value = 0
payment at the end of each month = 10,467.73676.
interest rate = 18% per year / 12 = 1.5% per month.
payments are made at the end of each month.
calculator says that the present value is equal to 597,115.126.
that's the outstanding remaining balance after 50 payments.
i did the analysis in excel and it confirms the results.
here's the display of the excel month by month analysis.
you can do the same analysis with the following online calculator if you don't have one available.
< rel=nofollow HREF= "https://arachnoid.com/finance/" target = "_blank">https://arachnoid.com/finance/
there are also formulas you can use at the following reference.
https://www.algebra.com/algebra/homework/Finance/THEO-2016-04-29.lesson#formulas
formula you would use are:
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.
and then:
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.
when you use the online calculator:
if you enter the present value as positive, the payment will show up as negative.
interest rate are in percent form, just as i did using the TI-BA-II.
results are rounded to the nearest penny, unlike what the TI-BA-II gives me.
when you use the formulas.
interest rate is not in percent form.
that means that 18% would be shown as .18 and 1.5% would be shown as .015.
all numbers are positive.
all parentheses need to be entered in your calculator exactly as shown.
if you have any problems or questions on any of this, write to dtheophilis@gmail.com.
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