Find the required annual interest rate to the nearest tenth

Find the required annual interest rate to the nearest tenth of a percent for $65,000 to grow to $65, 783.91 if interest is compound quarterly for 6 months.

Solution

A=P(1+(r_/n))^nt

compunded quarterly

A=accumulated amount =65783.91,P=principle amount =65000, t in years =6/12 =0.5 year, n =number of times compounded in year =4

65783.91=65000(1+(r/4))^4*0.5

65783.91=65000(1+(r/4))²

(1+(r/4))²=65783.91_/65000

(1+(r/4))²=1.012060154

(1+(r/4))=1.006012

(r/4)=0.006012

r=4*0.006012

r=0.024048

r=2.4048%

required annual rate of interest =2.4%