Math 142 Section 1.3 Examples

Math 142
Section 1.3 Examples
Example 1: We deposit $1200 into a bank account for 9 months, and withdrew $1270. What was
the interest rate for the account?
Example 2: Suppose $1000 is deposited in an account earning interest at 6% per year, compounded
monthly. How much money will be in the account after 5 months?
Math 142
Section 1.3 Examples
Example 3: Suppose we invest $1200 for 3 years at 8% per year. How much do we have at the
end, if we compounded a) quarterly?
b) monthly?
Example 4: Suppose Fred wants to take a trip to Europe at the end of his college career. If Fred
needs $4,500 for this trip, how much would he need to deposit into an account paying 6.8% year
compounded daily if he expects to graduate 4 years from now? How much interest did he earn?
Math 142
Section 1.3 Examples
Example 5: Solve for x: 9x = 274x−10 .
Example 6: Suppose 4 years from now I want to buy a Death Star that costs $5000. I have an
account with continuously compounded interest at an annual rate of 4%. How much money should
I put into the account now in order to reach my goal?
Example 7: A bank advertises a nominal rate of 6.3% compounded quarterly. What is the effective
yield of an account here?
Example 8: What is the effective rate of the account for my Death Star?
Math 142
Section 1.3 Examples
Example 9: Bank A advertises an account with a nominal rate of 7.1% compounded semiannually.
Bank B has an account with a annual rate of 6.9% compounded continuously. What are the effective
rates of these accounts? Which one is better for your money?
Example 10: Suppose the population of a colony in 1790 is 3926 thousand people. Analysis of
the population shows that it is increasing in population by 3.3% per year. Write a function P (x)
for the population of the colony (in thousands).
Example 11: Suppose you place $1000 under your mattress and left it there. Meanwhile, inflation
continues at a rate of 3% per year. Comparatively, how much would this $1000 be worth in 5 years?
(ie, what is the real purchasing power of this $1000 in terms of the present amount?)