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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. ๐
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
Thank you for your help.
Practice Q:
Gerard Jones plans to save for his 5year 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.
Your answer was Wrong.
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
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For example, if you want to do 11,562 * (1.08)^2 on your calculator, the steps are:
Type โ1.08โ then hit the โyหxโ button, followed by โ2โ, then the change sign key “+/“, then the โ=โ 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 (รท ), 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







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