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# Level 1 - Time Value of Money

Hello- I have a question. This problem has too many steps.

Is there a quicker way to do Step 1 & 2?

On Step 2,

I am not familiar about -1,-2, ...etc or how to do this on calculator. :(

6 10,805 10,805 (1.08)-1 =10,004

7 11,562 11,562 (1.08)-2 =9,912.5

8 12,371 12,371 (1.08)-3 =9,820.5

9 13,237 13,237 (1.08)-4 =9,729.6

10 14,163 14,163 (1.08)-5 =9,639

SUM = USD 49,106

Practice Q:

Gerard Jones plans to save for his 5-year doctorate degree, which starts 6 years from now. The current annual expenditure is USD7,200 and it is expected to grow by 7 percent annually. Gerard will need to make the first payment 6 years from today. He identifies a savings plan that allows him to earn an interest of 8 percent annually. How much should Gerard deposit each year, starting one year from today? Assume that he plans to make 5 payments.

A USD8,370.

B USD8,539.

C USD8,730.

Explanation:

A is correct. This problem can be solved in three steps.

Step 1: Find the annual expenditures

Annual Expendituret=6=7,200 (1+0.07)6=USD10,805

Annual Expendituret=7=7,200 (1+0.07)7=USD11,562

Annual Expendituret=8=7,200 (1+0.07)8=USD12,371

Annual Expendituret=9=7,200 (1+0.07)9=USD13,237

Annual Expendituret=10=7,200 (1+0.07)10=USD14,163

Step 2: Find the present value of annual expenditures at t = 5

Time Period Annual Expenditure (USD) Present Value

6 10,805 10,805 (1.08)-1 =10,004

7 11,562 11,562 (1.08)-2 =9,912.5

8 12,371 12,371 (1.08)-3 =9,820.5

9 13,237 13,237 (1.08)-4 =9,729.6

10 14,163 14,163 (1.08)-5 =9,639

SUM = USD 49,106

Step 3: Find the annuity payment

N = 5, %i = 8, PV = 0, FV = 49,106, CPT PMT.

PMT = 8,370.

• Hi @fmccray

Let's see if I can help on this as your Step 2 notation doesn't seem correct.

So in your Step 2, I've copied and amended the calculations to show you that x^-2 = 1/(x^2), so you can calculate in 2 ways in essence using the y^x key on your BA II plus (assuming you're using this) and parenthesis "(" & ")" functions on your BA II plus :

Step 2: Find the present value of annual expenditures at t = 5

Time Period Annual Expenditure (USD) Present Value

PV of 10,805 (at t=6) to t=5: 10,805 * (1.08)^-1 =10,004 = 10,805 / (1.08)

PV of 11,562 (at t=7) to t=5: 11,562 * (1.08)^-2 =9,912.5 = 11,562 / (1.08)^2

PV of 12,371 (at t=8) to t=5: 12,371 * (1.08)^-3 =9,820.5 = 12,371 / (1.08)^3

PV of 13,237 (at t=9) to t=5: 13,237 * (1.08)^-4 =9,729.6 = 13,237 / (1.08)^4

PV of 14,163 (at t=10) to t=5: 14,163 * (1.08)^-5 =9,639 = 14,163 / (1.08)^5

SUM = USD 49,106

-------------------------------

For example, if you want to do 11,562 * (1.08)^-2 on your calculator, the steps are:

Type “1.08” then hit the “yˆx” button, followed by “2”, then the change sign key "+/-", then the “=” sign. Then with the answer (0.8572), just multiply ("x" button) that with 11562, to get 9912.55.

Alternatively, if you want to do 11,562/(1.08)^2, you can type it as: 11562, then divide sign (÷ ), then "(1.08", "y^x", then "2", then ")", then "=", which should get you the same 9912.55 answer.

Does this help? I'm not sure if there is a faster way to compute step 1 and 2 though

• Thank you so much. what you showed me to do on the calculator is really helpful. I sure appreciated it.

I has hoping that there is a quicker way to do step 1 & 2. :)

• No worries, glad it helped a little. It's probably a speed thing for Step 1 and 2, hopefully you'll get there after loads of practice! But agree it seems quite a lot of steps for the amount of time you have each question...

• i am having difficulties understanding these kinds of question, would you be able explain why are we calculating the PV?

• My BA 2 Plus calculator hangs whenever I try to calculate interest rate for TVM reading. I clear TVM in calculator every time when I attempt the problem. Can this issu be resolved or should I buy a new calculator?

• How does it 'hang'? Sometimes it takes a while to calculate and the screen is just blank while it processes. Is that the problem you're having?