Are you assuming that, when payments are made at the beginning of each year, there are a total of nine payments made? (The last payment would be made on the date the balloon payment was due.) With payments made at the end of the year, there would only be eight payments. This, as well as the extra year of earning interest on each deposit when paid at the beginning, makes a big difference in the answer.
The normal use of the term "balloon payment" refers to a situation where a large portion of the original principal is paid off at the end of a loan payment period. Some such loans are "interest-only" loans, with the full iniital balance paid off at the end. Since you provided no information on how much of the initial balance is paid off at the end, I assume you are amortizing the loan with equal annual payments. Please let me know if that is not the case.
Here is how to do the nine-payment, annual compounding, case, with payment P at the beginning of each year.
P [ (1.07)^8 + (1.07)^7 + (1.07)^6 + (1.07)^5 + (1.07)^4 +(1.07)^3 +(1.07^2 + (1.07)1 + 1] = $1,500,000
P * [ 1.71819 + 1.60578 + 1.50073 + 1.40255 + 1.31080 + 1.25504 + 1.14490 + 1.07000 + 1.0000] = $1,500,000
12.31209 P = $1,500,000
P = $121,831.47
With payment at the end of each year and annual compounding, there are 8 payments P due and
P [(1.07)^7 + (1.07)^6 + (1.07)^5 + (1.07)^4 +(1.07)^3 +(1.07^2 + (1.07)^1 + 1] = $1,500,000
P* 10.59390 = $1,500,000
P = $141,590.92
The semiannual-compounding case works similarly, but I'd like to wait to hear from you before doing the numbers. Receiving semiannual componding at 7% annual rate is the equivalent of receiving (1.035)^2 = 1.07123 of your money at the end of a year, or 7.123% annual interest compounded annually.
No, I did not use a formula such as you described. I am not sure what you mean by Fv and Pv.
If you mean
(Final Value) = (1+i)^8 * (Initial investment),
that would apply to a case where you deposit the money once, at the beginning and let it grow, with no annual payments. I treated a case where you make equal annual payments that result in full payoff at the end of the 8 years.
Unless I get a clearer statement of the problem, including whether there is an extra payment at the end (when you pay at the beginning of each year) and how much the final balloon payment amount is, I can't be sure we are talking about the same problem.
<<for the eight payments do you have to do them seperatley or was this done all together as one >>
In the example I showed, I added up the compound balances resulting from each annual payment. That is why I had to add a sum of terms. You could consider that as "doing them separately".
If you got 136,000 for the first part, approximately, you were probably assuming eight payments, with no payment at the end of the final year. In that case, if you make the payments at the beginning of each year,
P [ (1.07)^8 + (1.07)^7 + (1.07)^6 + (1.07)^5 + (1.07)^4 +(1.07)^3 +(1.07^2 + (1.07)^1 ] = $1,500,000
P * [ 1.71819 + 1.60578 + 1.50073 + 1.40255 + 1.31080 + 1.25504 + 1.14490 + 1.07000] = $1,500,000
10.97799 P = $1,500,000
P = $136,637.05
With eight payments made at the end of each year, the annual payment P required is the $141,590.92 amount I derived earlier. The difference is $4953.87 more to be paid per year if one waits until the end of the year to make a payment.
If you think that's the way the problem should be interpreted, let me know and I will do the semiannual compounding case. The payments will be less in that case.
By the way, this is what would be alled a "sinking fund" situation, not a balloon payment. The payments indicated above would have to be made in addition to equal "interest only" annual payments of $105,000, in order to have $1,500,000 available in the sinking fund at the end of the eight years, to pay off the principal of the original loan.