Answer to Question #204850 in Financial Math for Sesethu Ntoni

Question

Question 11

Siya wants to buy a new state of the art computer for R35 000. He decides to save by depositing an amount of R500 once a month into an account earning 11,32% interest per year, compounded monthly. The approximate time it will take Siya to have R35 000 available is

[1] 70 months.

[2] 40 months.

[3] 115 months.

[4] 54 months.

[5] none of the above.

Question 12

The accumulated amount after eight years of monthly payments of R1 900 each into an account earning 9,7%

interest per year, compounded monthly, is

[1] R274 069,25.

[2] R182 400,00.

[3] R126 532,64.

[4] R395 077,74.

[5] none of the above.

Question 13

Vanessa decides to invest R140 000 into an account earning 13,5% interest per year, compounded quarterly. This new account allows her to withdraw an amount of money every quarter for ten years after which time the account will be exhausted. The amount of money that Vanessa can withdraw every quarter is

[1] R3 500,00.

[2] R1 704,28.

[3] R6 429,28.

[4] R8 594,82.

[5] none of the above.

Answer 1

(11)The time that will be taken by a monthly investment can be ascertained by using the 'Nper' function in Excel. The time taken to accumulate the sum of R35,000 is ascertained below.

Thus, option [4] 54 months is correct.

(12)

$PN=\frac{d((1+\frac{r}{k})^{Nk}−1}{\frac{r}{k}}$

• P_N is the balance in the account after N years.
• d is the regular deposit (the amount you deposit each year, each month, etc.)
• r is the annual interest rate in decimal form.
• k is the number of compounding periods in one year.

$PN=\frac{1900((1+\frac{0.097}{12})^{8\times12}−1}{\frac{0.097}{12}}$

$PN=\frac{1900((1+0.0.008083)^{96}−1}{0.008083}$

$=R274 069.25.$

Ans [1] R274 069.25

(13)Given present value is R140000 = P

Rate of interest per year is 13.5%

For quarterly, n = 13.5/4 = 3.375% = 0.03375

Number of years i = 10 years

For quarterly, i = 10$\times$ 4 = 40

We know that , P = x[1-(1+i)^-n]/i

P*i/[1-(1+i)^-n] = x

x = 140000*0.03375/[1-(1+0.03375)^-40]

x = 4725/[1-0.265]

x = 4725/0.735

x = 6429.28

Thus, The amount of money Vanessa can withdraw every quarter is R6429.28.

So, Option 3 is correct.