Answer to Question #196937 in Financial Math for Beauty Magadlela

Question

Three years ago Thokozile borrowed R7 500 from Alfred. The condition was that she would pay him back in seven years’ time at an interest rate of 11,21% per year, compounded semi-annually. Six months ago she also borrowed R25 000 from Alfred at 9,45% per year, compounded monthly. Thokozile would like to pay off her debt four years from now .

After seeing what she must pay Alfred, Thokozile decides to reschedule her debt as two equal payments: one payment now and one three years from now. Alfred agrees on condition that the new agreement, that will run from now, will be subjected to 10,67% interest, compounded quarterly. The amount that Thokozile will pay Alfred three years from now is

[1] R22 286,88.

[2] R25 103,93.

[3] R32 500,00.

[4] R21 171,35.

[5] none of the above. 

Answer 1

Present value of debt:

$PV=FV/(1+r)^n$

where FV is future value,

r is interest rate,

n is number of periods in the future.

$PV_1=\frac{7500}{(1+0.1121/2)^{4\cdot2}}=R\ 4848.25$

$PV_2=\frac{25000}{(1+0.0945/12)^{3.5\cdot12}}=R\ 17982.90$

Payment now (payment of 1st debt for three years and 2nd debt for six months):

$PV_1+PV_2=4848.25+17982.90=R\ 22831.15$

The rest of debt:

$25000+7500-22831.15=R\ 9668.85$

Payment three years from now:

$9668.85(1+0.1067)^{3\cdot4}=R\ 32500$

Answer: [3] R32 500,00