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Before starting each calculation make sure you clear your calculator! This is a very important habit to get into. Use these Keystrokes to clear: (F, CLX, F, X>Y).
1. Trevor purchased an investment for $25,000. He expects it will increase in value at a rate of 10% compounded annually for the next 5 years. If his expectations are correct how much will his investment be worth at the end of the 5th year?
Answer: $40,262.75
This calculation is as straightforward as it gets for TVM questions. That said, many students still make a simple error. Fortunately, that error is easy to correct. From an early age we are taught to enter percentages into calculators as decimals. By this logic, we enter 50% as 0.5, 35% as 0.35, 7% as 0.07 and so on. This is not how you should enter percentages into the HP 12c, which actually automatically converts percentages for us. If 0.1 is entered into the i register the calculator will solve for 0.1% instead of 10%. Enter the percent as a full round number.
Keystrokes: (10, i)
Let's enter the Present Value next. Trevor is starting off with $25,000. This is our Present Value of the investment. He is paying that money to have it invested so we need to enter it as a negative number by pressing the CHS button.
Keystrokes: (25,000, CHS, PV)
He is investing it for 5 years. This is our time frame.
Keystokes: (5, n)
He is not making any other payments into the account during the 5 year period so we will leave the PMT field blank and the calculator will automatically assign it a value of 0. Now all we have to do is press FV and the calculator will give us our answer!
Answer: $40,262.75
2. You are offered a $105,000 mortgage at an annual interest rate of 7.3% compounded monthly. How much must you pay each month to completely repay the loan in 30 years?
Answer: -$719.85
Let’s start off by entering in the easy known variables for this equation. You are offered a mortgage of $105,000, this is the present value of the loan so we want to enter it into the PV input.
(105,000 then PV)
Our goal is to pay off the mortgage completely, so we will want to enter 0 as our future value input.
(0 then FV)
Here is where it can get a bit tricky! The payments are over a span of 30 years, this is our time frame and what we would usually input for the n key. However, the question mentions that the interest is compounded monthly. As such, we need to input the time frame into the calculator as 12-month periods. Pressing the blue g key on the calculator before pressing the n key will automatically divide the 30 years into a period of 360 months. Notice that the blue lettering on the bottom of each button corresponds to the function applied when you press the blue g key first.
(30 then g then n)
Since the payments have been input on a 12-month cycle, we also need to input the 7.3% interest on a 12-month cycle. The blue g key comes to our rescue with this as well. Remember, with financial calculators we enter interest as a whole number instead of as a decimal like with regular calculators.
(7.3 then g then i)
Now all that’s left is to solve the equation! Press (PT) to find out what your monthly payment needs to be to pay off the mortgage. Note that the number will be negative because we are paying that much each month. It is a negative cash flow, so the answer will be negative.
Answer: -$719.85
3. Abby’s grandmother invests $1,000 into a mutual fund for Abby on the day she is born. The fund is remarkably consistent and earns 2.3% annually. How much will the fund be worth when Abby’s grandmother gifts her the fund on her 18th birthday?
Answer: $1505.78
This question can trip people up right from the get go! Abby’s grandmother invested $1,000 on the day she is born, $1,000 is our present value of the investment. Because Abby’s grandmother paid the $1,000 to the mutual fund company to have it invested we need to set it to be a negative number to reflect the negative cash flow. If we do not set the payment to negative it will cause our answer to come out negative instead. If you get a question on the CFP exam and one answer option is positive and the other is negative be extra careful that you are setting your input variable correctly!
The CHS button on your HP12C will turn a negative number positive, or a positive number negative.
(1000 then CHS then PV)
Abby’s grandmother plans to gift the fund on Abby’s 18th birthday, 18 is our time frame.
(18 then n)
The fund is remarkably consistent and returns 2.3% annually. This means it’s a simple matter of entering 2.3 into the i input. While consistency like this would never happen in the real world, we are just looking for comprehension of how the equation works. Try not to get too hung up on questions with scenarios that are unrealistic or farfetched.
(2.3 then i)
Now all that is left is to solve the equation! Press the (FV) key to find out the future value of the fund after the 18 years.
Answer: $1505.78
4. David’s goal is to become a millionaire by the time he is 40 years old. On his 25th birthday he decided to make a plan to reach his goal. If he already has $50,000 in an investment returning 7% annually, how much must he contribute at the beginning of each month to reach his goal by his 40th birthday?
Answer: -$2,689.84
At first glance this question looks more difficult than it really is. Start with the solid goals and figures that we know and work your way back to the correct answer. We know that David’s goal is to be a millionaire so enter $1,000,000 for our future value.
(1,000,000 then FV)
We know that he already has $50,000 invested, this is our present value. Remember that he paid money to have it invested so we need to set this to be a negative number to reflect that it is being paid out.
(50,000 then CHS then PV)
At this stage in solving the problem many students get discouraged or lost. Stay focused on what is being asked in the question and you will be able to find the right answer every time! The question is “how much must David contribute MONTHLY in order to reach his goal?” This tells us that we need to break our time frame up into 12 month increments as well as break the interest rate into 12 month increments to take account of the monthly contributions. David is 25 now which means he has 15 years until he turns 40. Remember that by pressing the blue g key before hitting the n key will automatically divide the years into 12 month increments for you.
(15 then g then n)
Now we have to enter the interest rate. He is receiving 7% annually, but because he is making monthly contributions we need to have the interest rate reflect that by also dividing it into 12-month increments. The g key will also solve this problem for us by pressing it before we hit the i key to input the interest rate.
(7 then g then i)
Now that we have all our known variables input into the calculator we just have to solve for the equation right!? Not so fast. There is still one clue in the question we have not addressed yet. The question asks how much David needs to contribute at the beginning of each month, this figure will be different from the answer if David was contributing at the end of each month thanks to the power of compounding interest. To tell our calculator that David is making beginning of month contributions we have to set our payments to BEG which you can see in the little blue lettering underneath the 7 key. If the question said the payments came at the end of the month you would take the same actions except you would press the 8 key for END instead.
(g then 7 then PMT)
Answer: -$2,689.84
5. Kiesha has been investing $2,000 at the end of each year for the past 11 years to make a down payment on a vacation home. Assuming she has earned 8% compounded annually on her investments, how much does she have saved today?
Answer: $33,290.97
This question is pretty straightforward, one thing that can trip people up is the use of present and past tense though. The question asks, “how much does Kiesha have saved today?” so we need to solve for present value right? Wrong! Even though the question is phrased in a way that leads us to believe it is looking for the present value, the information that is provided to us forces us to actually solve for future value.
Let’s go through the problem step by step to demonstrate this. First let’s start with the easy known variables. We know that the interest rate is 8% so let’s enter that first.
(8 then i)
We know that she has been saving for 11 years so let’s enter that next. Don’t forget it says she makes the investments at the end of each year so make sure your calculator is set for END and not BEG.
(11 then n)
We also know that she makes yearly payments of $2,000. Remember that it’s a payment so don’t forget to set it to be a negative number.
(2,000 then CHS then PMT)
Here is where it starts to get tricky. Many students will think “I have all my known variables entered, all I have to do is hit PV and I will get the answer!” and they will have the calculator return $14,277.93. This answer is incorrect. Remember the calculator needs 4 variables entered in order to solve for the 5th. So far we have only entered 3 variables. When we hit PV the calculator assumes that the missing 4th variable is 0 and it will save that to the FV memory. What we just did was solve for how much money Keisha would need now if she wanted to make $2,000 payments for the next 11 years at an 8% interest rate. While interesting, its not really what we are trying to figure out right now.
What we need to be aware of and look out for is the hidden variable of 0. While the question does not explicitly say so, we can assume that Keisha is starting her savings from scratch as there is no mention of prior savings. Therefor we need to enter 0 into PV because that is the baseline she is starting out from. Do not let past and future tense wordings on questions confuse you. Think about the known variables, be aware of the “hidden 0” variable, and work out the answer from there.
(0 then PV)
Now we solve for FV and we end up with the correct answer.
Answer: $33,290.97
