Question

How much money should be invested in an account that earns 9% interest, compounded monthly, in order to have $16,000 in 4 years? (Round your answer to two decimal places.)

Answer 1

How much money should be invested in an account that earns 9% interest, compounded monthly, in order to have $16,000 in 4 years? (Round your answer to two decimal places.)

Remember that

The compound interest formula is equal to

`A=P(1+(r)/(n))^(nt)`

where

A is the Final Investment Value

P is the Principal amount of money to be invested

r is the rate of interest in decimal

t is Number of Time Periods

n is the number of times interest is compounded per year

in this problem we have

A=$16,000

r=9%=9/100=0.09

n=12

t=4 years

substitute the given values in the formula

`16,000=P(1+(0.09)/(12))^(12\cdot4)`

solve for P

`\begin{gathered} 16,000=P((12.09)/(12))^(48) \\ P=\$11,177.83 \end{gathered}`