Answer to Question #196935 in Financial Math for Beauty Magadlela

Question

A savings account pays interest at the rate of 5% per year, compounded semi-annually. The amount that should be deposited now so that R250 can be withdrawn at the end of every six months for the next ten years is

[1] R3 144,47.

[2] R6 386,16.

[3] R1 930,43.

[4] R3 897,29.

[5] none of the above

Answer 1

Given Amount to be withdrawn every six months is R250 = x

Rate of interest, i = 5%

For six months , i = (5/2)% = 2.5% = 0.025

Given Time, n = 10

For six months, n = 10*2 = 20

We know that present value of series of payments is P = x[1-(1+i)^-n]/i

Now P = 250[1-(1+0.025)^-20]/0.025

P = 250[1-0.61]/0.025

P = 250(0.39)/0.025

P = 250*15.589

P = R3897.291

Thus, R3897.29 should be deposited so that R250 can be withdrawn at the end of every six months for the next ten years.

So, option 4 is correct.