Answer to Question #189564 in Financial Math for ntombi mshango

Question

Andile deposits R900 into a savings account paying 6,5% interest per year, compounded quarterly. After three and a half years he withdraws R1 000 from the account and deposits it into a second account paying 11% simple interest per year.

How much is the total amount accrued in the first account two years after withdrawing the R1 000? The correct answer, rounded to the nearest rand, is

[1] R145.

[2] R1 105.

[3] R605.

[4] R128.

[5] none of the above

Answer 1

The amount accrued after 3 and 1/2 yrs is

 A = P(1 + r/n)^nt

= 900.00(1 + 0.065/4)^(4)(3.5)

= 900.00(1 + 0.01625)⁽¹⁴⁾

= R1,127.85

After the withdrawal of R1000, the remaining amount is

= R1,127.85 - R1000

= R127.85

The amount accrued in the first account two years after withdrawal is

A = P(1 + r/n)^nt

= 127.85(1 + 0.065/4)⁽⁴⁾⁽²⁾

= 127.85(1 + 0.01625)⁽⁸⁾

= R145.45

Rounding off the answer is R145