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Finance: Compound Interest and Annuities
If interest is compounded a finite number of times per year, then the compound interest calculations can be
done with the Finance application on the TI-83/84.
TI-83: FINANCE is above the x-1 key.
TI-83+/TI-84: FINANCE is accessed using the APPS button
The TVM Solver is the most common Finance application, as it finds the Time Value of Money.
The TVM Solver uses positive numbers for money received (inflow) and negative numbers for money
paid (outflow) from your perspective. Money borrowed will be positive and money invested will be
negative. Neglecting this issue may result in incorrect answers or calculator errors.
The most common compounding frequencies are:
Compounding
Annually Semi-Annually Quarterly Monthly Weekly Daily
# of times per year (m)
1
2
4
12
52
365
Part I
1. A savings account starts with a balance of $500 and earns 6% annual interest compounded annually.
How much is in the account after 5 years?
Solution Method:
i. Go to FINANCE
ii. Choose TVM Solver
iii. TVM Solver Screen
Enter values for each of the following variables:
N = total number of compounding periods = ______ years * _____ times/year (m) = _________
I% = interest rate AS A PERCENT = _______
The FINANCE application is the only time we ever use percents without converting to decimals.
PV = principal = present (starting) value = __________ (Enter this value as a negative number
because the money is leaving your hands, i.e., outflow.)
PMT = dollar amount of regular payments made = 0
FV = future (ending) value = ?
(Enter 0 here as a placeholder for a moment.)
P/Y = number of payments per year
C/Y = number of compounding periods per year (m)
P/Y and C/Y will ALWAYS be the same in this class.
P/Y = C/Y = m = _________
PMT: END for ALL questions we cover in class
Move the cursor back to FV. Press ALPHA and then ENTER to solve.
Note: The calculator will put the symbol by this value after solving.
a. What is the future value of the account (rounded to the nearest cent)? FV = _____________
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Finance: Compound Interest and Annuities
Interest is the difference between the initial account balance and the future value.
b. How much interest did the account earn (rounded to the nearest cent)? ___________
For the remainder of this activity, round all answers that involve money to the nearest cent.
2. A savings account earned 8% annual interest compounded quarterly for the past 7 years and currently
has a balance of $8500. What was the initial amount in the account if no additional deposits were
made?
a. Which variable are you solving for in the TVM Solver? _______ Put a ? by this value below.
b. Enter the following values:
N = total number of compounding periods = ______ years * _____ times/year = _________
I% = _______
PV = present (starting) value = ________
PMT = regular payments made = 0
FV = future (ending) value = ________
P/Y = C/Y = # of compounding periods per year = ________
c. Solve for PV by moving your cursor back to PV. Press ALPHA and then ENTER.
What was the initial amount in the account? __________ How much interest was earned? __________
3. You deposit $1000 in an account paying 9% annual interest compounded daily. How long will it take
for the value of the account to double, assuming no additional deposits are made?
a. Which variable are you solving for in the TVM Solver? _______ Put a ? by this value below.
b. Enter the remaining values and solve for the unknown:
N = _____ I% = _____
PV = _________
PMT = 0
FV = ________
P/Y = C/Y = ________
Be sure to enter PV as a negative value or you will get an error. Refer back to Page 1 for details.
c. It will take __________ days for the account to double. (Round to the nearest day.)
d. Convert this time period to years and days. Time to double is _______ years and _______ days.
4. How much interest is earned in one year on $10,000 if the account pays 5.5% annual interest
compounded
annually? ________________
monthly? ________________
semi-annually? _______________
weekly? _______________
quarterly? _______________
daily? _______________
As the number of compounding periods per year increases, the interest earned per year increases, but there
is a limit to how much interest can be earned.
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Finance: Compound Interest and Annuities
Part II
1. Ben would like to have $60,000 available for college in 18 years.
a. If an account exists earning 7% annual interest compounded annually, how much should be
deposited now to have the $60,000 in 18 years?
b. How much interest is earned?
If you don’t have all the money available now, you can save a bit each year to reach this goal. This
is a type of annuity.
An annuity is an account into which regular payments are made. The annuities in this class
are all CERTAIN and SIMPLE, meaning:
The payments are made at fixed time intervals.
The periodic payments are of equal size.
The payments are made at the end of the interval.
The interest is paid at the end of the interval.
c. Use the TVM Solver to find the amount of the annual payments that should be deposited into an
account earning 7% annual interest compounded annually in order to reach the goal of $60,000.
N = _____
I% = _____
PV = 0
PMT = ?
FV = ____________
P/Y = C/Y = _____
The amount of the annual payments is _________________.
d. In total, how much money was deposited into the account? 18*PMT = _________________
e. Interest Earned = Final Value of the Account – Amount Deposited =
________________ − ________________ = __________________
f. Why are the interest amounts in parts b. and e. different?
2. You are saving for retirement by depositing $400 per month in an account that earns 8% annual interest
compounded monthly. What are the total amount in the account and the total interest earned if this is done
for 10 years? For 30 years?
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Finance: Compound Interest and Annuities
Loans also deal with making payments. A bank loans you money and you make regular payments until you
no longer have any of the bank’s money. This means that the original value of the loan is the present value
(PV) and the future value of the loan (FV) is 0.
3. You find a car advertised for no money down with payments of $199 per month for 72 months. In the
fine print you see that the interest is 9% annual interest compounded monthly on the unpaid balance.
a. What is the purchase price of the car? That is, how large was the loan you took out?
Hint: You need to solve for PV.
b. How much money total will you pay out of pocket? 72*199 = ______________
c. Interest Paid = Amount of Money Repaid – Amount Borrowed =
________________ − ________________ = __________________
4. Your goal is to retire when you become a multi-millionaire ($2,000,000), so you start saving $100 per
week in an account that pays 10% annual interest compounded weekly. If you start at age 23, how old
will you be when you retire?
5. A cello costs $998. You purchase the cello on credit and pay it off by making payments of $39.00 per
month for 3 years.
a. What annual interest rate compounded monthly were you charged (rounded to 4 decimal places)?
b. How much interest do you pay in total?
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