Answer to Question #208097 in Financial Math for Beauty Magadlela

Question

Thulisile bought a house and managed to secure a home loan for R790 000 with monthly payments of R9 680,70 at a fixed interest rate of 13,75% per year, compounded monthly, over a period of 20 years. If an average yearly inflation rate of 9,2% is expected, then the real cost of the loan (the difference between the total value of the loan and the actual principal borrowed) is

[1] R201 642.

[2] R270 749.

[3] R588 358.

[4] R1 060 749.

[5] R87 126

Answer 1

We need to calculate total value of loan by using inflation rate. We need to use this formula

Total value of loan $=\frac{PMT}{r}\times[1-\frac{1}{(1+r)^n}]$

 Where

PMT=monthly payment of loan

r= periodic rate of interest

n=number of periods

Calculation of total value of loan

Monthly payment(PMT) $=9680.70$

Monthly interest rate(r) $=\frac{9.2\%}{12} =0.76666667 =0.0076666667$

Number of periods $=20\times12 =240$

Total value of loan $=\frac{PMT}{r}\times[1-\frac{1}{(1+r)^n}]$

              $=(\frac{9680.70}{0.0076666667})\times[1-\frac{1}{(1+0.0076666667)^{240}]}\\ =1,262,700\times[1-\frac{1}{6.2525070977}]\\ =1,262,700[1-0.159935844]\\ =1,262,700\times 0.840064156\\ =1,060,749$

Total value of loan is R1,060,749

Calculation of the real cost of the loan

Real cost of the loan =Total cost of loan -Actual principal borrowed

                $=R1,060,749 -R790,000\\ =R270,749$

option [2] R270,749. is correct