If a person borrows $2,400 and repays the loan by paying $200 per month to reduce the loan and 1% of the unpaid balance each month for the use of the money, what is the total cost of the loan over 12 months?

\text { Define the sequence }\left(a_{n}\right)_{n \geq 1} \text { recursively by } a_{1}=1 \text { and } a_{n+1}=\sqrt{2+a_{n}} \text { for all } n \geq 1 \text { i. Prove that for all } n \geq 1 \text { we have } 1 \leq a_{n} \leq 2 \text { ii. Prove that }\left(a_{n}\right)_{n \geq 1} \text { is a monotonic sequence. } iii. Deduce that the sequence converges with limit 2. iv. Show that for all n > 1 we have 2-a_{n} \leq \frac{1}{(2+\sqrt{3})^{n-1}}

How long will it take money to quadruple if it is invested at the following rates? A) 7.3% compounded daily ) 14.6% compounded daily

Use the formula for simple interest, I = Prt, to find the indicated quantity. Assume a 360 day year. 1=$18; P $1200; t=90 days; r =?

Some friends tell you that they paid $14,666 down on a new house and are to pay $640 per month for 30 years. If interest is 5.7% compounded monthly, what was the selling price of the house? How much interest will they pay in 30 years?

You can afford monthly deposits of $230 into an account that pays 3.6% compounded monthly. How long will it be until you have $6,100 to buy a boat?

1: List the first five terms of the given sequence. a_{n}=\frac{n(n+1)}{2} \cos (n \pi)

1. Show that for all m < n E N and all 2 < k < n E N, \frac{1}{m^{k}}\left(\begin{array}{c} m \\ k \end{array}\right)<\frac{1}{n^{k}}\left(\begin{array}{l} n \\ k \end{array}\right) \leq \frac{1}{k !} 2. Use the binomial theorem to show that a_{n}:=\left(1+\frac{1}{n}\right)^{n} is a strictly monotone increasing sequence.

4. (12 points) Determine whether the series listed below are convergent or divergent. Give the sums of the convergent series. \text { a. } \sum_{i=1}^{\infty} \frac{e^{i}}{3^{i-2}} \text { b. } \sum_{n=1}^{\infty} \frac{4}{n^{2}+4 n+3}+\frac{3^{n-1}}{4^{n}} \text { c. } \sum_{k=1} \ln \left(\frac{n}{n+3}\right) \text { d. } \sum_{n=1}^{\infty} \ln n-\ln (1+2 n) \text { . }

Use the continuous compound interest formula to find the indicated value. A=$19,390; P=$13,700; t = 60 months; r = ?