Rob deposits $600 monthly into an account that pays 4% per 6 months, and the fir

Question

Rob deposits $600 monthly into an account that pays 4% per 6 months, and the first deposit is made today. After 8 deposits, Rob decided to deposit $590 into the account, starting from the 9th deposit, and he deposit $ 10 less into this account until the last deposit becomes $ 100, then no further deposit is made. At the beginning of the year 1, Rob would like to withdraw $X out from this account every 6 months

Determine the value of X that allow Rob to withdraw money out indefinitely. Round the answer to the nearest dollar

Explanation / Answer

So, Rob has been investing 600$ Monthly for the 1st 8 months and than from 9th month every month he pays 10$ less from the previous month till his last installment becomes 100$ and 4% interest is being paid every 6 Months.

For this first of all one need to find out the total number of installments Rob is going to make.

Total Installments=

8 Installments of 600$

(+) 50 Installments of reduced payments i.e. (600-100)/10

So, Total 58 Installments.

Here assuming compounding interest rate of 4% per 6 months which is compounded than find out the value for each instalment as under:

For 1st installment:600*(1+(0.04/6))=604

For 2nd installment: (600+604)*(1+(0.04/6))=1212

For 3rd Installment: (600+1212)*(1+(0.04/6))=1825

Like wise, after 58th Installment the final value would be approx. 28,248 $

And on 60th month the value of the investment would be 28,625$.

and if Rob wants to withdraw X amount for the indefinate time every 6 months than he can withdraw $1145 (28,625*4%) every 6 months assuming that he will withdraw amount for the first time in 60th Month as interest amount get credited every 6 months only.

Related Questions

Navigate

• Browse (All)
• Browse R
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.