(Related to The Business of Life: Saving for Your First House) (Future value) You are hoping to buy a house in the future and recently received an inheritance of $18 comma 000. You intend to use your inheritance as a down payment on your house. a. If you put your inheritance in an account that earns 9 percent interest compounded annually, how many years will it be before your inheritance grows to $32 comma 000? b. If you let your money grow for 9.75 years at 9 percent, how much will you have? c. How long will it take your money to grow to $32 comma 000 if you move it into an account that pays 4 percent compounded annually? How long will it take your money to grow to $32 comma 000 if you move it into an account that pays 12 percent? d. What does all this tell you about the relationship among interest rates, time, and future sums?

A) We need to determine the n in the following equation: FV = PV (1 + r)ⁿ

r = 9% ; FV = 32,000 ; PV = 18,000

32,000 = 18,000 (1.09ⁿ)

32,000 / 18,000 = 1.09ⁿ

1.7778 = 1.09ⁿ

n = (log 1.7778) / (log 1.09) = 6.68 years

B) FV = 18,000 (1.09⁹°⁷⁵) = 18,000 x 2.32 = $41,704

C) if r = 4% ; FV = 32,000 ; PV = 18,000

n = (log 1.7778) / (log 1.04) = 14.67 years

if r = 12% ; FV = 32,000 ; PV = 18,000

n = (log 1.7778) / (log 1.12) = 5.08 years

D) The higher the interest rate, the shorter it takes for money to grow to a certain amount. The higher the interest rate, the more money you will have after a certain amount of years.  

its simple as this, microeconomics is the study of economics at an individual, group or company level, macroeconomics on the other hand, is the study of a national economy as a whole.

hope it =^-^=

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