In this video we will answer
the given annuity questions using the TI-84 TVM Solver.
Suppose you want to have $500,000
for retirement in 30 years.
Your retirement account earns
4% interest compounded monthly.
For part a, how much would you need to deposit
in the account each month?
And part b, how much interest
would you earn over the 30 years?
Let's begin by determining the required information below
for the TVM Solver.
Capital N is the total number of payments
over the 30 years and because the payments are monthly,
capital N is the number of months in 30 years,
which is 30 times 12 which is equal to 360.
I is the annual percentage rate of return which is 4%.
And therefore I% is four.
PV stands for present value, or starting amount.
When the account is first opened the balance is zero,
the present value is zero.
We are solving for PMT, the monthly payments,
and we'll come back to this.
FV stands for future value.
Because you want $500,000
in 30 years, 500,000 is the future value.
PY and CY stands for payments per year
and compounds per year.
Because the payments are monthly and the interest
is compounded monthly, both are 12.
And we always leave the PMT option
at the bottom on end not begin.
And now we grow the calculator and enter the information.
We press apps.
Enter on the finance option and enter on the TVM Solver.
And now we enter the information.
Capital N is 360, enter.
The percentage is four, enter.
Present value zero, enter.
We'll come back to the payment.
Future value is 500,000
enter.
And both payments per year and compounds per year are 12.
If we press 12 and then enter notice how 12
is automatically entered for the compounds per year.
Now we go back up to the payment row.
To solve for the payment we press alpha enter
and round to the nearest cent.
Notice how it is negative because this represents
the money you have to pay each month
to reach your financial goal.
And therefore, the monthly payment or deposit
would have to be $720.41.
So now we know you would have to deposit $720.41 each month.
For part b, how much interest
would you earn over the 30 years?
To determine the amount of interest earned
we would take the balance of $500,000
and subtract all of the monthly deposits of $720.41,
which means the interest earned over the 30 years
is equal to $500,000
minus the monthly payment of $720.41
times the number of monthly payments over the 30 years
which would be 30 times 12 because each year has 12 months.
And now going to the calculator.
We go back to the home screen
by pressing second mode for quit.
And we enter 500,000 minus 720.41 times 30 times 12
which is 360,
giving us the interest earned over the 30 years,
which is $240,652.40.
And now for part c.
If you wait and only have 20 years to try to reach
the same financial goal,
what would you need to deposit each month?
So going back to the table below,
the payment is going to change,
and capital N is also going to change
because now capital N is going to be the number of months
in 20 years which is 20 times 12, or 240.
Everything else remains the same.
So going back to the calculator you press apps,
enter, enter, change capital N to 240.
Go down to the payment row because
everything else stays the same and press alpha enter.
And now the monthly payment would have to be $1363.23.
Again, now you would need to deposit $1363.23
each month to reach the same financial goal.
And then part d, how much interest
would you earn over this 20 year period.
To determine the interest we take the ending balance
of $500,000 and subtract out the monthly deposits
of $1363.23 which would be 1363.23
times the number of monthly deposits over the 20 years,
which is 20 times 12.
So going back to the calculator.
Second mode takes us back to the home screen,
and we enter 500,000 minus 1363.23 times 20 times 12,
which is 240.
Enter.
The interest earned is $172,824.80.
I hope you found this helpful.