Answer to Question #197946 in Financial Math for Beauty Magadlela

Question

Percy deposits R100 into a bank account earning interest at an interest rate of 18% per annum, compounded monthly. The time (in months) that it will take the account to accumulate to R20 000 is given by

[1] n = ln[200(1,015)] 0,015 .

[2] n = ln[200(0,015) + 1] ln(1 + 0,015) .

[3] n = ln[200(1,015) + 1] − ln(1,015).

[4] n = ln[200(0,015) − 1] ln(1 + 1,015) .

[5] none of the above.

Answer 1

A =R 20,000

R = (18/12 )%

= 1.5 %

A = p(1+r/100)ⁿ

20,000 = 100(1+0.015)ⁿ

(20,000/100) = 1.015ⁿ

200 = 1.015 ⁿ

Introducing indices,

In 200 = n In 1.015 therefore,

n = ln[200(0,015) − 1] ln(1 + 1,015)

Choice 4 is correct