Find the required annual interest rate to the nearest tenth

Find the required annual interest rate, to the nearest tenth of a percent, for $50,000 to grow $100,000 if interest is compounded continuously for 25 years.

Solution

2) we know the compounded interest formula is A=P(1+r/n)^(nt)

we have given Amount A=$25,580 and Principal P=$15000 ,time t=12years interest is compounded monthly

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

25,580=15000*(1+r/12)^(12*12) since n=12 months t=12years

(1+r/12)^144 =25,580/15000

1+r/12=(25,580/15000)^(1/144)

1+r/12=1.003713549

r/12 =(1.003713549-1)

r=12*(1.003713549-1)=0.045

r=(45/1000) *100=4.5%

r=4.5%