Answer to Question #196940 in Financial Math for Beauty Magadlela

Question

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

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*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.