Ok.. AP's and GP's are now a thing of the past (what?? huh?? when did that happen - in 8A of course!).. we're now onto applications of growth and decay.. nope.. (we did that in 8A too.. huh?? what??)..

MAT 8B We're now onto Annuities and Amortisation - growth and decay with payments.

The calculator handles this under the Financial, Sequences or Spreadsheet.

Starting with Financial:

Once in Financial, select Compound interest.

n - represents the number of installment periods

I% - is the interest p.a.

PV - is the present value (the initial investment)

PMT - is the payment per period

FV - is the future value (the investment at period N)

P/Y - is the number of installment periods per year (how often a payment is made)

C/Y - is the number of times interest is compounded

Let's look at a simple problem say 8B q.3 in 3A MAT. Kelvin invests $620,000 into an account giving 5.8% pa. interest compounded annually from which her withdraws $50,000 at the end of every year.

a) How much is left after 10 withdrawals (N=10, FV=?).

N=10

I%=5.8

PV=-620000

PMT=50000

P/Y=1

C/Y=1

Leave the cursor on FV and press solve (at the bottom left hand corner of the window)

FV=436670

b) For how many years will Kelvin be able to withdraw 50000 per year

Find when the account is exhausted of funds (eg. N=? when FV=0)

I%=5.8

PV=-620000

I%=5.8

PMT=50000

FV=0

P/Y=1

C/Y=1

Leave the cursor on N and press solve (at the bottom left hand corner of the window)

N=22.52 therefore for 22 years.

If anyone can explain why PV is negative I would be very appreciative. I know from last year's course that it is but have no idea why.

Now Sequence:

This could also have been done through the Sequence tool using recursion

a) Tn+1=Tn*1.058-50000; T0=620000. Find T10

b) Tn+1=Tn*1.058-50000; T0=620000. Find n Where Tn=0

I'll leave the spreadsheet method for another day.

Here is a link to other CAS calculator posts.

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