Answer to Question #217500 in Financial Math for Shakhina

Question

John graduated from college and began working in the family restaurant business. At the end of the third month of the first year he began putting R7440.00 per annum in an individual retirement account and contributed to it for a total of ten years. The account interest at 11% per annum, compounded quarterly. The amount that was available to him after ten years is...

Answer 1

To calculate amount for first year rate will be divided by 4 ie 11%/4=2.75% to get n which is number of years 3/4x4=3 since he didn't save for the first quarter of that year.Therefore we will use the formula A=P(1+r/100)ⁿ the principal p will therefore be R7440 the rate r will be 2.75% n will be 3 therefore A=R7440(1+2.75/100)³ =R8070.83

We shall be taking the previous year amount we add R7440 to be the principal of next year n will be 4 but rate remain 2.75% therefore

2nd year A=(R8070.83+R7440)(1+2.75/100)⁴ =R17288.7

3rd year A=(R17288.7+R7440)(1+2.75/100)⁴=R27563.1

4th A=(R27563.1+R7440)(1+2.75/100)⁴ =R39015.2

5th year A=(R39015.2+R7440)(1+2.75/100)⁴=R51779.95

6th year A=(R51779.95+R7440)(1+2.75/100)⁴=R66007.8

7th year A=(R66007.8+R7440)(1+2.75/100)⁴ =R81866.48

8th year A=(R81866.48+R7440)(1+2.75/100)⁴=R99542.9

9th year A=(R99542.9+R7440)(1+2.75/100)⁴ =R119245.4

10th year A=(R119245.4+R7440)(1+2.75/100)⁴=R141206.25

R141206.25 will be the amount after ten years