# Rates of change - loan

The formula for the loan one can get with a payment of $P paying monthly for 15 years at an interest rate of r is:

L=(12P/r)[1-(1+(r/12))^(-180)]

a.) Find dL/dt, the rate of change of the loan with respect to time.

(Here, t is the time that is passing, not the t in the original function if you know the loan. Treat P as a function of time and r as a function of time since one's possible payment changes with time and the interest rate definitely changes with time.)

b.) A certain person can now make a payment of $1200 per month, and his monthly payment is increasing at a rate of $85 per year. Given that the interest rate is now 5.75% and is increasing at a rate of 0.5% per year, find how the amount of loan this person can get is changing at this moment.

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#### Solution Preview

a) Since P and r's functions of time is not given, we assume that P=P(t) and r=R(t)

First we find dL/dP= ...

#### Solution Summary

There are two questions in this solution regarding rate of change and loans.