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# Recurrence Relation : Compound Interest

1. Pauline takes a loan of S dollars at an interest rate of r percent per month, compounded monthly. She plans to repay the loan in T equal monthly installments of P dollars each.

a) Let a(subscript n) denote the amount Pauline owes on the loan after n months. Write a recurrence relation for a (subscript n).
b) Solve the recurrence relation that you obtained in a), above.
c) Use your answer from b) to obtain a formula for the monthly payment, P.

#### Solution Preview

recurrence relation

Please show all work and explain steps for my own understanding.

1. Pauline takes a loan of S dollars at an interest rate of r percent per month,
compounded monthly. She plans to repay the loan in T equal monthly installments
of P dollars each.
a) Let a(subscript n) denote the amount Pauline owes on the loan after n months. Write a recurrence relation for a (subscript n).
Assume that the amount Pauline owes on the ...

#### Solution Summary

A recurrence relation is used to solve a compound interest problem. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.

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