1. ## Need help...recursion/finite sets

PLz help me do these problems...thank youuu sooo much.

1) An amortized loan is paid off in equal periodic payments of P units. Assume that the periodic interest rate over the time period is (100 X r)%. If L is the loan amount and Xn is the balance remaining after the nth payment, give a recursive formula for Xn.

comment: usually one is given L and r, and the objective is to find a value of P such that the balance is equal to zero after the Mth payment for some fixed M (which is normally a multiple of 12). In order to do this, one needs to derive a closed formula for Xn and solve for P in terms of L, r, and M.

Finite Sets:

1) Determine the number of Boolean subalgebras of P(X) if X is the set {1,2,3,4}. How many have exactly two atomic subsets?

2. Originally Posted by jenjen
PLz help me do these problems...thank youuu sooo much.

1) An amortized loan is paid off in equal periodic payments of P units. Assume that the periodic interest rate over the time period is (100 X r)%. If L is the loan amount and Xn is the balance remaining after the nth payment, give a recursive formula for Xn.

comment: usually one is given L and r, and the objective is to find a value of P such that the balance is equal to zero after the Mth payment for some fixed M (which is normally a multiple of 12). In order to do this, one needs to derive a closed formula for Xn and solve for P in terms of L, r, and M.
As $X_n$ is the debt after the n-th payment the amout owing
before the $n+1$-st payment is $(1+r)X_n$, so:

$
X_{n+1}=(1+r)X_n - P.
$

RonL