I'm trying to calculate the interest and total of money when :
Someone is loaning $3600 every year over 11 years with an interest of 10% ?
Like : 3600 + 10% = 3960 first year, 3960+3600+10% = 8316 second year etc.
Just that I need a formula to calculate it faster because it's a hurdle with the calculator.
Best Answer
The accumulated value of a cash flow under compound interest can be calculated by regarding each individual payment separately, then taking the sum of their accumulated values at the same time point.
In your case, the first payment of $3600$ has had $11$ years to compound interest at an $i = 0.10$ annual effective rate, thus its accumulated value at the end of the term is $3600(1.1)^{11}$. The second payment has had $10$ years to compound interest under the same rate, so its accumulated value is $3600(1.1)^{10}$; and so forth. The total accumulated value of $11$ such annual payments just before the eleventh would be paid, would then be $$3600\left((1.1) + (1.1)^2 + \cdots + (1.1)^{11}\right) = 3600 (1.1) \frac{ {1.1}^{11} - 1}{{1.1}-1}.$$ In actuarial terminology, this is the accumulated value of a 11-year level payment annuity-due of $3600$ per year with annual effective interest rate of $i = 0.10$, and has actuarial notation $$3600 \ddot s_{\overline{11}\rceil 0.10}.$$
Of course, I am making some assumptions because certain facts were not stated in the question. In particular,