# Recurrence relation for amount in account at end of n years if no money withdrawn.

• Mar 26th 2011, 06:59 AM
mujix
Recurrence relation for amount in account at end of n years if no money withdrawn.
A deposit of 50000 O.R.is maid to an investment fund at the beginning of a year.On the last day of each year two dividends are awarded.The first dividend is 20% of the amount in the account during that year. The second dividend is 45% of the amount in the account in the previous year.

(a)Find a recurrence relation for {pn}, where pn is the amount in the account at the end of n years if no money is ever withdrawn.

hope someone can help me, and thanks in advance.
• Mar 26th 2011, 09:00 AM
SpringFan25
You didn't specify where you were stuck, so i'll assume its at the first step.

The amount of money at the end of year n is going to be the amount of money at the end of the previous year + dividends received in that year.
• Mar 27th 2011, 06:07 AM
CaptainBlack
Quote:

Originally Posted by mujix
A deposit of 50000 O.R.is maid to an investment fund at the beginning of a year.On the last day of each year two dividends are awarded.The first dividend is 20% of the amount in the account during that year. The second dividend is 45% of the amount in the account in the previous year.

(a)Find a recurrence relation for {pn}, where pn is the amount in the account at the end of n years if no money is ever withdrawn.

hope someone can help me, and thanks in advance.

Let \$\displaystyle \$\$p_n\$ be the amount in the account at the end of the \$\displaystyle \$\$n\$ th year.

Now you need to write \$\displaystyle \$\$p_{n+1}\$ in terms of \$\displaystyle \$\$p_n\$ and \$\displaystyle \$\$p_{n-1}\$.

Try that let us know how you get on and what problems you are still having.

CB