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Course: M 119, Fall 2009School: IUPUI
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119 Extra MATH Exercises For Section 4.3 By: Ma a n O mr a n 1) Suppose $1000 is invested at an annual interest rate of 8%. Compute the balance after 10 years in each of the following cases:: a) the interest is simple interest b) the interest is compounded quarterly c) the interest is compounded continuously. (Ans: 1800, 2208.04, 2225.54) 2) How quickly will money double if it is invested at an annual interest...
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119
Extra MATH Exercises For Section 4.3
By: Ma a n O mr a n
1) Suppose $1000 is invested at an annual interest rate of 8%. Compute the balance after 10 years in each of the following cases:: a) the interest is simple interest b) the interest is compounded quarterly c) the interest is compounded continuously. (Ans: 1800, 2208.04, 2225.54) 2) How quickly will money double if it is invested at an annual interest rate of 8% and the interest is compounded: a) quarterly b) continuously (Ans: 8,75 years, 8.66 years) 3) One bank offers interest rate of 6.1% compounded quarterly, and another bank offers interest rate of 6% compounded continuously. Which bank offers better deal? (use the effective rate rule) (Ans: 0.0624, 0.0618 therefore the first offers better deal 6.24%) 4) How much should you invest now at an annual interest rate of 8% so that your balance 20 years from now will be $10000 if the interest rate is compounded: a) quarterly b) continuously (Ans: 2051.10, 2018.97) 5) A bank compounds interest quarterly. What (nominal) interest rate does it offer if $1000 grows to $2203.76 in 8 years? (Ans: 10 percent) 6) Which investment has greater effective rate: 10.25% per year compounded semiannually or 10.20% per year compounded continuously? (Ans: 10.51% , 10.74%) 7) How quickly will money triple if it is invested at a rate of 6% compounded semiannually? (Ans: 18.58 years) 8) Determine which of the two rates gives the better return: a) 8% compounded monthly or 8.2% compounded semiannually. b) 10% compounded quarterly or 9.9% compounded monthly c) 10% compounded annually or 9.6% compounded monthly d) 10% compounded annually or 9.51% compounded daily. (Ans: a. 0.0830 & 0.0837 b. 0.1038 & 0.1036 c. 0.10 & 0.1003 c. 0.10 & 0.0998 ) 9) How much money should be invested today at 12% rate compounded monthly in order to have $4000 at the end of 5 years? (Ans: $2.201.80) 10) What principal P invested at 8.4% compounded quarterly will accumulate to a value of $4800 at the end of 12 years? (Ans: $1770.13)
11) What principal P invested at 8.4% simple interest will accumulate to value a of $4800 at the end of 12 years? (Ans: $2390.44) 12) How long will it take $1000 to grow to $4800 if it is invested at 10% compounded continuously? (Ans: 15.68 years) 13) At what rate of interest compounded annually will an investment of $2100 accumulate to $3400 by the end of 6 years? (Ans: 8.36%) 14) At what rate of interest compounded monthly will an investment of $1000 accumulate to $3000 by the end of 15 years? (Ans: 7.45%) 15) At what rate of interest compounded continuously will an investment of $1000 accumulate to $3000 by the end of 15 years? (Ans: 7.32%) 16) Jack borrowed $5000 from Jim, promising to pay back $7000 at the end of 2 years. What rate compounded monthly was Jack paying? (Ans: 16.94%) 17) Amy invested $2500 in a saving account. Find its value at the end of 8 years if it earned 7.3% compounded daily the first 4 years and 7.9% compounded daily the last 4 years. (Ans: $4591.59) 18) How long does it take amount to double at 8.5% compounded: a) semiannually b) continuously (Ans: 8.33 years, 8.15 years) 19) It is determine that the value of a machinery declines exponentially. A machine that was purchased 5 years ago for $65,000 is worth $35,000 today. What will be the value of the machine 5 years from now? (Ans: $18846.15) 20) In 1985 the cost of a prime rib dinner was about $9.00. In 1988, the cost was $12.00. If the cost is growing exponentially, what will be the cost in 1994? (Ans: $21, k= 0.096) 21) Find the present value of $1000 payable in 3 years if the money is invested at 14% compounded continuously. (Ans: $657.05) 22) Investment A is currently worth $70,200 and is growing at the rate of 13% compounded continuously. Investment B is currently worth $60,000 and is growing at the rate of 14% compounded continuously. After how many years will the two investment have same value? (Ans: 15.7 years) 23) The price of houses in a certain city are dropping. The price of a house was $150,000 in 1980 and $120,000 in 1990 (decline). Assume the price is decreasing according to the exponential-decay, find the price of the house in 1995? (Ans: $107,332)
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