A Different Approach to Compound Interest

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A Different Approach to Compound Interest
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Many questions about financial transactions can
be dealt with using the Compound Interest Formula
.
We now consider a different way of looking at
compound interest. We will extensively use the
TVM solver of your TI calculator.
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• To access this feature of your calculator,
  proceed as follows
• TI-83 or TI 84
• Select APPS, Finance, TVM Solver
• TI-83
• Select 2nd, x-1, TVM Solver

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Time Value of Money Solver
Open the TVM solver and see the variables

• N
• I
• PV
• PMT
• FV
• P/Y
• C/Y
• PMTEnd Begin.

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Defining the TVM variables

• N Total number of compounding periods
• I Annual interest rate
• PV Present value of money
• PMT Payment amount per compounding period
• FV Future value of money
• P/Y Number of payments per year
• C/Y Number of compounding periods per year

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Remarks about using the TVM Solver

• P/Y will always be the same as C/Y.
• Interest is entered in percent, not in decimal
  form.
• Cash inflows (money received) must be entered
  as positive numbers
• and cash outflows (money paid) must be entered
  as negative numbers.
• At the bottom of the TVM Solver menu, make sure
  that End, not Begin, is always highlighted.

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We now consider a few of examples.

• In each one, try to see
• how we interpret information to put in the TVM
  solver
• how we interpret information obtain from the TVM
  Solver

The emphasis is on getting used to the TVM Solver
variables
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Example An old problem revisited
Jane is 21 and wants to have 10,000 on her 25th
birthday. How much money does she have to invest
at 6 interest compounded monthly to achieve her
goal?
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We need to know PV, the present value.
Since interest is compounded monthly, C/Y12
and P/Y12.
Over the 4-year period, there will 4 times 12
compounding periods, so N48.
After 4 years, Jane will receive 10,000, hence
FV10000.
Note that we enter a positive number for cash to
be received.
The annual rate of interest is 6, so I6.
Jane will not be making any payment, therefore,
PMT0.
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We now proceed to find PV. Set PV0.
Place the cursor in PV0. Press the ALPHA key
(underneath the 2nd key), then the SOLVE key
(same as the Enter key)
You should see on your screen

• PV -7870.98

The negative sign indicates that Jane must invest
(cash outflow) 7,870.98 in order to accumulate
10,000 in 4 years.
Remark We set PV equal to 0 , and then solve .
But you can actually set PV equal to anything
that you want, and then solve.
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Example
Jim is the beneficiary of a trust fund
established for him 21 years ago at his birth.
If the original amount placed in the trust was
10,000, how much will he receive if the money
has earned interest at the rate of 8 per year
compounded quarterly?
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We need to know FV, the future value.
Since interest is compounded quarterly, C/Y4
and P/Y4.
Over the 21-year period, there will 21 times 4
compounding periods, so N84.
10,000 was invested so PV -10000.
Note that we enter a negative number for cash
outflow.
The annual rate of interest is 8, so I8.
No payment will be made, therefore, PMT0.
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We now proceed to find FV. Set FV0.
Place the cursor in FV0. Press the ALPHA key
(underneath the 2nd key), then the SOLVE key
(same as the Enter key)
You should see on your screen

• PV 52773.32

The positive sign indicates that Jim will receive
at age 21 the sum of 52,773.32 from the trust
fund.
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Example
Joe puts 2,000 into a savings account that earns
interest at a rate of 4.5 compounded daily.
How long will it take him to triple his
investment?
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We need to know N, the number of compounding
periods.
Since interest is compounded daily, C/Y360 and
P/Y360.
2,000 was invested, so PV -2000.
Note that we enter a negative number for cash
outflow.
When the investment triples, its value is 6,000.
Hence FV 6000.
Note that we enter a positive number for cash
inflow.
The annual rate of interest is 4.5, so I4.5.
No payment will be made, therefore, PMT0.
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We now proceed to find N. Set N0.
Place the cursor in N0. Press the ALPHA key
(underneath the 2nd key), then the SOLVE key
(same as the Enter key)
You should see on your screen

• N8789.45

It will take 8,789 compounding periods, in this
case, days. Dividing by 360, we see that it will
take about 24 years.