# mathmatics

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on the first day of march, a bank loans a man £2500 at a fixed rate of intrest of 1.5percent per month. this intrest is added on the last day of the month and is calculated on the amount due the first day of the next month.the man agrees to make repayments on the first day of each month and each repayment is £300 exept for the smaller final amount which will pay off the loan.

a) the amount that he owes at the start of each month is taken to be the amount still owing just after the monthly repayment has been made.

So, let Un and Un+1 represent the amounts that he owes at the start of two successive months. write down a recurrence relation involving Un+1 and Un.

B) find the date and the amount of the final payment.

• mathmatics -

looks like they want you to do it step by step, what a bother.

Here is the actuarial mathematical way of doing it.

2500 = 300[1 - 1.015^-n]/.015
.
.
1.015^-n = .875
using logs
n = 8.9

So he needs 8 full payments of £300

outstanding balance just after making the 8th payment
= 2500(1.015)^8 - 300(1.015^8 - 1)/.015
=

= 286.38

(notice the 8.9 indicated we were very close to another payment of 300)

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