Answer to Question #196926 in Financial Math for Beauty Magadlela

Question

Thando invested R10 000 in a special savings account on 15 May at an interest rate of 15% per year, compounded every three months for seven months. Interest is calculated on 1 January, 1 April, 1 July and 1 October of every year.

If simple interest is used for the odd periods and compound interest for the rest of the term, ,the amount of interest received by Thando after seven months is

[1] R901,35.

[2] R1 644,57.

[3] R896,95.

[4] R665,54.

[5] none of the above.

Answer 1

"R 901.35" answers is correct.

For first, 3rd ,fifth and 7th months. The simple interest shall be calculated using

I = PRT/100 ..for the months 2 ,4 and 6th we shall use the formula

P(1+r/100) raised to power t. In which p(principal) ,r(rate) and t( time/period)

The rate per month is 15/12

= 1.25%

For month 1: (10000*1.25*1)/100

=R125

Month 2:( R10125*1.0125)-10125

=126.56

Month 3 :

(10251.56*0.0125)

=126.14

Month 4:

(10379.70*1.0125)-10379.

=127.66

Month 5:

10509.45*0.0125

=131.37

Month 6 :

(10640.82* 1.0125)-10640.82

=130.00

Month 7th :

10773.82*0.0125

= 134.67.

Total interest shall therefore be:

134.67+130.00+131.37+127.66+126.14+126.56+ 125

=901.40~ 901.35