Compound Interest An account is established with a principal

Compound Interest An account is established with a principal of $200, paying 4% interest compounded semiannually How long will it take for the balance to reach $300? Tripling Money How long does it take for money to triple in an account paying 5% interest compounded annually? Doubling Money An account paying interest compounded continuously at a rate r doubles in size every 12 years. Find r. Competing Accounts Suppose that Bob deposits $1000 into an account paying 6% interest compounded quarterly at the same time that Janet deposits $1200 into an account paying 6% interest compounded annually How long will it take for Bob\'s balance to exceed Janet\'s? Competing Accounts Suppose that $200 was deposited on January 1. 2002, into an account that earned 5% interest compounded annually. Suppose further that $200 was deposited on January 1, 2003, into a different account that earned 6% interest compounded annually In what month of what year will the balance in the account earning 6% interest overtake the balance in the account earning 5%? Competing Accounts On January 1, 2003, $1000 is deposited into an account paying 15% simple interest, and $100 is deposited into an account paying 5% interest compounded annually In what month of w hat year will the balance in the simple interest account be overtaken by that in the compound interest account? Compact Disk Inflation Suppose that the average price of a compact disk was $18.00 on January 1, 2003, and that the price increases at the rate of 3% per year. Give the month and the year in which the average price of a compact disk will be $100 Annual Inflation Suppose that inflation is 3.5% annually Then goods or services that cost P dollars today will, on the average, cost P(1.035)^t dollars in t years If tuition at a certain prestigious university is $25,000 per year in 2004-05, in what year will tuition reach $40,000? Consumer Price index Consumer price Index (CPI) was 99.6 in 1983 and 172.2 in 2000. In other words, goods and services that cost $99.60 in 1983 cost $172 20 in 2000. Assuming exponential growth, what will the CPI be in 2010? When will it reach 300? Dollar Devaluation One dollar in 2000 was worth approximately 17 in 1960 dollars. Assuming this is an exponential decrease, when will a dollar be worth 1 in 1960 dollars? Population Growth At 8:00 A M, July 4, 2006, a colony of 1000 of the smallest free-living entity, Mycoplasma laidlawii (average weight = 10^-16 grams), is established If the population were to double every hour, at what lime would the collective mass of the colony exceed that of the largest animal on Earth, the 190-ton blue whale? Population Decline The population of a certain endangered species of owl is declining exponentially. There are currently 500 living specimens, whereas just 10 years ago there were 10,000. If lire population continues to decline exponentially, how long will it be until there is only a single owl left? Population Decline The metropolitan area encompassing Steubenville. Ohio and Weirton. West Virginia suffered the greatest percentage population loss in the United States between 1990 and 2000 (Data source: U.S. Bureau of the Census.) The population of Steubenville-Weirton was 142, 523 in 1990 and 132,008 in 2000. Assuming the population is decreasing exponentially, what will the population be in the year 2010? Population Growth The fastest growing metropolitan area in the United States between the years 1990 and 2000 was Las Vegas. Nevada-Arizona (Data source U.S Bureau of the Census.) The population was 852, 737 in 1990 and 1, 563, 282 in 2000. Assuming exponential growth, what will the population be in the year 2010? Carbon Dating Physicists found that the remains of a certain woolly mammoth contained only 25% of its original carbon-14 Given that the half-life of carbon-14 is 5760 years, how old is the mammoth? Carbon Dating The well-preserved corpse (see photo) of a Bronze Age man was found frozen in ice in the Austrian Alps in September 1991. If only 53.3 % of the carbon-14 is found and the half-life of carbon-14 is 5760 years, how old is the

Solution

35) P = $200 ; r = 4% = 4%/2 = 2% compounded semi annually

Amount = P(1 + r/2)^2n

300 = 200(1 +0.02)^2n

ln1.5 = 2n*ln1.02

n = ln1.5/2ln1.02 = 10.237 years

27) Compounding continously :

A = Pe^(rate*time)

2P = Pe^(r*12)

2 = e^12r

take natural log on both sides:

ln2 = 12r

r = 0.0577

rate ; r = 5.77%