Answer to Question #204854 in Financial Math for Sesethu Ntoni

Question

Question 1

Siphesihle borrows money from the bank at a discount rate of 16,5% per year. He must pay the bank R30 000 in eight months from now. The amount of money he receives from the bank now is

[1] R33 707,87.

[2] R26 700,00.

[3] R27 027,03.

[4] R33 463,26.

[5] R33 300,00.

Question 2

Phathu needs R10 500 in ten months' time to buy herself a new lens for her camera. Two months ago she deposited R9 000 in a savings account at a simple interest rate of 11,5% per year. How much money will Phathu still need to buy the lens ten months from now?

[1] R465,00

[2] R229,50

[3] R637,50

[4] R408,67

[5] None of the above

Answer 1

Solution: for questions 1

Time, t = 8 months = 8/12 year = 2/3 year

Discount rate, r = 16.5% per year = 0.165

Let M be the borrowed money from the bank.

And D be the discounted amount.

Then, $D=M.r.t$

$\Rightarrow D=M(0.165)(2/3) \\\Rightarrow D=0.11M ...(i)$

Now, $P=30000$

$P=M-D \\ \Rightarrow 30000=M-0.11M$ [Using (i)]

$\Rightarrow 0.89M=30000 \\\Rightarrow M=33,707.87$

Hence, option 1, i.e., R 33707.87 is correct.

For questions 2

Amount required after 10 months = R10,500

Two months ago amount deposited = R 9000

Interest Rate =11.5%

Interest rate per month (r)$= 11.5\%/12 = 0.958333 = 0.00958333$

Months of compounding for 9000 is 10+2 (n)= 12

Therefore, amount after 10 months $= 9000\times(1+r)^n$

$=9000\times(1+0.00958333)^{12}$

$=9000\times[1.12125928]$

$=10091.33$

Therefore, Amount required $=10500 - 10091.33 = 408.67$

The correct answer is  4.     R 408.67