Question

Davis decides to think about retirement and invests at the age of 30 . He invests $5,000 and hopes the investment will be worth $250,000 by the time he turns 70 . If the interest compounds continuously, approximately what rate of growth will he need to achieve his goal? Round to the nearest tenth of a percent.

Answer 1

Rate of growth he will need to achieve his goal is 9.8%

Explanation:

Principal=$5,000

Time(t)=70-30=40 years

Period (n)=12 months

Interest rate (r)=?

A=$250,000

r=n{(A/P)^1/nt - 1}

=12{(250,000/5000)^1/12*40 - 1}

=12{(50)^1/480 - 1}

=12{(50)^0.0021 - 1}

=12(1.0083 - 1)

=12(0.0082)

=0.0984

r=0.0984*100

=9.84%

To the nearest tenth=9.8%