1. A savings account with a current balance of $5,000 earns 2.75% annual interest, compounded continuously. To the nearest dollar, what will be the account balance in 10 years?

GROWTH.

a=?,P=5,00,r=2.75,t=10

A=P(1+rt)

A=5,000(1+2.75*10)

A=5,000(1+27.5)

A=5,000(28.5)

A=142,500

Since the balance is $5000 and earns 2.75% annual interest, the money will increase. 2.According to the U.S. Census Bureau (http://www.census.gov/), the population of Texas is growing at a faster rate than any other state in the United States. In 2012 the population of Texas was approximately 26,000,000 people and was growing at a rate of 2.10% per year. At the current growth rate, what will the population of Texas be in the year 2030? Round the answer to the nearest million people. (Note: Use continuous compounding.) 3.The value of a new car decreases exponentially. Suppose you buy a new car for $32,000, and the value of the car decreases at a rate of 20% per year. Find the value of the car after 5 years. Round the answer to the nearest thousand dollars.

DECAY

v = future value

c = current value

r = depreciation rate per period

t = number of periods

—

v = 32000*(1-0.20)^5

v = 10485.764.Suppose you deposit $10,000 into a savings account with 3.5% compound interest compounded each month. Find the account balance in 50 years. Round the answer to the nearest thousand dollars.

GROWTH

v = final value

p = initial (principal) value

r = interest rate (as a decimal)

n = number of compounding periods per year

t = number of years

—

v = 10000( 1 + (0.035/12) )^(12*50)

v = 57399.665.On January 1, 2010, the population of a small town called Riley was 1,250. Its population has been decreasing at a steady rate of 8% per year. According to this model, what was Riley’s population on January 1, 2000? Round the answer to the nearest person. (Hint: Use the continuously compounding formula.) DECAY

A = Pe^rt

A = 1250

r = -0.08

t = 10

1250 =…

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