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Question 963142: How do I calculate the following......Kate has bought a house and managed to secure a loan for R600 000. The term of the loan is 20 years and
the applicable interest rate is 10,5% per year, compounded monthly. Determine Kate’s monthly payment.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! well, you can use a financial calculator.
the value of the mortgage on the house is 600,000.
the nominal interest rate is 10.5% per year.
the effective interest rate is 10.5/12 = .875% per month.
the length of the loan is 20 years * 12 = 240 months.
the payments are assumed to be made at the end of each month.
the calculator will tell you that the payments will be 5,990.279322 per momth.
if you don't have a calculator, then you will need to use the annuity from a present amount formula.
that formula is:
pmt = [pv * i * (1+i)^n] divided by ((1+i)^n - 1)
pmt is the monthly payment.
pv is the present value of the mortgage which is equal to 600,000.
i is the interest rate per time period.
since the time periods are in months, and since interest rate is interest rate percent divided by 100, then i is equal to 10.5 / 100 / 12 which is equal to
.00875.
n is the number of time periods which is equal to 12 * the number of years which then becomes 240 which is equal to the number of months of the morgage.
the formula of pmt = [pv * i * (1+i)^n] divided by (1+i)^n - 1 becomes:
pmt = (600,000 * .00875 * 1.00875^240) / (1.00875^240 - 1) which becomes:
pmt = 5990.279322.
if you use the online calculator that is part of the following link, then you would make the following entries.
pv = 600000
fv = 0
np = 240
pam = leave this blank
ipr = .875 ***** this is entered as a percent (10.5%/12 = .875%) - don't include the percent sign.
select payments made at end of time period.
http://www.arachnoid.com/lutusp/finance.html
the manually derive payment formula in the reference is slightly different than what i showed you above.
it includes fv in the calculation.
fv is future value of the payment.
since that is usually 0, it can be left out which is what i did above.
technically, it belongs there, so technically, the formula is:
pmt = [i * (pv * (1+i)^n + fv)] divided by ((1+i)^n - 1)
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