Question

Jeff has been offered a new job which requires that he invests $100

each month from his paycheck for his retirement and his company
gives him an additional 2% of the value of his account the end of every
month. How much will he have at the beginning of the 6th month?
WSW
ms
??
Account Balance
2% Interest Earned
Money Added
mmmm
0 $100 S202 $306.04
$4.04 $6.12
$100 $100 $100 $100
$2
b.
$412.16
$858.30
c.
d
$743.41
$520.40

Answer 1

At the beginning of 6th month , Jeff will have in his account $ 520 .

Explanation:

At the beginning of 6th month , Jeff will have in his account,

$
`( 100 * (1 + 0.02* 4) + 100 * (1 + 0.02 * 3) + 100 * (1 + 0.02 * 2) + 100 * (1 + 0.02) + 100)`

= $
`(100 * (5 + 0.02 * (4 + 3 + 2 + 1)))`

= $
`(100 * (5 + 0.02 * 10))`

= $
`(100 * 5.2)`

= $ 520

since, the $ 100 deposited at the end of 1st month earns interest for 4 months till the end of the 5th month, the $ 100 deposited at the end of the 2nd month earns interest for 3 months and so on till the last $100 deposited earns interest for '0' month.