What is a binomial? followed with an example?
2 answers:
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Part A)
![\bf \qquad \qquad \textit{Future Value of an ordinary annuity}\\ \left. \qquad \qquad \right.(\textit{payments at the end of the period}) \\\\ A=pymnt\left[ \cfrac{\left( 1+\frac{r}{n} \right)^{nt}-1}{\frac{r}{n}} \right]](https://tex.z-dn.net/?f=%5Cbf%20%5Cqquad%20%5Cqquad%20%5Ctextit%7BFuture%20Value%20of%20an%20ordinary%20annuity%7D%5C%5C%0A%5Cleft.%20%5Cqquad%20%5Cqquad%20%5Cright.%28%5Ctextit%7Bpayments%20at%20the%20end%20of%20the%20period%7D%29%0A%5C%5C%5C%5C%0AA%3Dpymnt%5Cleft%5B%20%5Ccfrac%7B%5Cleft%28%201%2B%5Cfrac%7Br%7D%7Bn%7D%20%5Cright%29%5E%7Bnt%7D-1%7D%7B%5Cfrac%7Br%7D%7Bn%7D%7D%20%5Cright%5D)
![\bf A=1200\left[ \cfrac{\left( 1+\frac{0.05}{1} \right)^{1\cdot 12}-1}{\frac{0.05}{1}} \right]\implies A\approx 19100.55](https://tex.z-dn.net/?f=%5Cbf%20A%3D1200%5Cleft%5B%20%5Ccfrac%7B%5Cleft%28%201%2B%5Cfrac%7B0.05%7D%7B1%7D%20%5Cright%29%5E%7B1%5Ccdot%20%2012%7D-1%7D%7B%5Cfrac%7B0.05%7D%7B1%7D%7D%20%5Cright%5D%5Cimplies%20A%5Capprox%2019100.55)
part B)
so, for the next 11 years, she didn't make any deposits on it and simple let it sit and collect interest, compounded annually at 5%.
part C)
well, for 12 years she deposited 1200 bucks, that means 12 * 1200, or 14,400.
now, here she is, 12+11, or 23 years later, and she's got 32,668.42 bucks?
all that came out of her pocket was 14,400, so 32,668.42 - 14,400, is how much she earned in interest.
part B)
so, for the next 11 years, she didn't make any deposits on it and simple let it sit and collect interest, compounded annually at 5%.
part C)
well, for 12 years she deposited 1200 bucks, that means 12 * 1200, or 14,400.
now, here she is, 12+11, or 23 years later, and she's got 32,668.42 bucks?
all that came out of her pocket was 14,400, so 32,668.42 - 14,400, is how much she earned in interest.