using the recurrence relation

Question

A person deposits Rs. 10, 000/- in a bank in a saving bank account at a rate of 5% per annum. Let Pn be the amount payable after n years, set up a recurrence relation to model the problem. Also using the recurrence relation, find amount payable after 7 years. Any one can help me please. i don't know how to use recurrence relation

Answer 1

In this case a recurrence relation is just a formula for calculating $P_{n+1}$ if you already know $P_n$. The value of the account increases by $5$% each year, so $P_{n+1}$ must be $P_n$ plus $5$% of $P_n$, or $$P_{n+1}=1.05P_n\;.\tag{1}$$

That’s the requested recurrence relation. You also know that $P_0=10,000$, so you use $(1)$ to calculate in turn $P_1,P_2,\ldots,P_7$.

Answer 2

Recurrence relation $$ P_{n+1} = P_n+ P_n\frac{5}{100}=P_n(1+\frac{5}{100})$$

$n$ integer and positive. $$P_n = 10,000(1+\frac{5}{100})^n$$