Answer to Question #204851 in Financial Math for Sesethu Ntoni

Question

Questions 9 and 10 relate to the following situation: 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.

Question 9

The amount of money that Thokozile will have to pay Alfred four years from now is

[1] R36 607,98.

[2] R45 181,81.

[3] R55 336,49.

[4] R48 032,20.

[5] R54 278,92

Question 10

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

(9)$A=P(1+\frac{r}{n}){nt}$

where P is the initial principal balance, r is the interest rate, n is the number of times interest is compounded per time period and t is the number of time periods.

for the first case

$=7500(1+\frac{0.01121}{2})^{2\times 7}\\=7500(1+0.05605)^{14}\\=\R16093.26$

the second case

$=25000(1+\frac{0.0945}{12})^{12\times 4.5}\\=25000(1+0.007875)^{54}\\=R38185.66$

total amount

$=16093.26+38185.66= R54 278,92$

answer [5] R54 278,92

(10)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