$200 invested at time 5. long. to You invest $500 in this account today. Find i if the account's value twelve 2) It is known that aft) is of the form at + b. If $100 invested at times accumulates to $172 at time 3, find the accumulated value at time 20 3) At a certain rate of simple interest. $1,000 will accumulate to $1.110 Exercises for Chapter 2 1) Suppose that the accumulation function for an account is a(t) = years from now is $1.250. after a certain period of time. Find the accumulated value of $100 ata rate of simple interest half as great over a period five times as 4) Suppose that aft) = at + 106. If Sx invested at time 0 accumulates $1,000 at time 10 and to $2.000 at time 20, find z. 5) At a certain rate of compound interest 100 will increase to 200 in years, 200 will increase to 300 in y years, and 300 will increase to 1,500 in 2 years. If 600 will increase to 1,000 in n years, find an expression for n in terms of x, y, and z. 6) Find the effective rate of compound interest and compound discount in each case a) A deposit of $340 accumulates to $400 at the end of one year. b) A deposit of $550 earns $23 interest in one year. 7) $450 is deposited at 5.6% annual simple interest. a) Write an expression to compute the accumulated value of the account at any time t. b) Graph this expression. What sort of function is it? c) Find an expression for the effective rate of interest earned in period n. d) Evaluate your expression c) for n = 1,2,3,. e) Graph the expression in c) over the range n=1 to n = 20. 8) $500 is deposited at 6.5% annual simple interest for ten years. What rate of annual compound interest will accumulate to the same amount as this account over this same time period? 9) $1 is deposited in each of two accounts for a period of one year. Account 1 earns 5% annual simple interest. Account 2 earns 5% compound interest. 10) How much must be deposted now in order to accumulate to $4,000 under each of the following scenarios? a) The account earns 5% simple interest and is left on deposit for five years. b) The account earns 5% compound interest and is left on deposit for five years. c) The account earns 5% compound interest for the first three years and then earns 5% simple interest for two more years. 11) Find the accumulated amount of a deposit of $600 in each case, a) The account earns 4.5% simple interest for seven years. b) The account earns 4.5% compound interest for seven years. 12) What monthly rate of interest is equivalent to the following? a) A quarterly rate of 4%. b) A weekly rate of 6% (assume four weeks exactly per month). c) An annual rate of 5%. 13) What is the effective rate of annual interest on a car loan advertised as 1.5% per month? 14) Compute the amount of interest paid in each case. a) $500 is borrowed for one year at 6% compound interest. b) $500 is borrowed for one year at 6% discount. 15) Convert as indicated a) Find i if d= .07. b) Find d if i = .07. 16) A borrower receives $560 and must repay $600 at the end of one year. a) What is the effective annual rate of discount? b) What is the effective annual rate of interest