please solve with steps there are two parts Part 1 is includ

please solve with steps.
there are two parts
Part 1 is included in picture

Part 2 is At 7% compounded continuously the investment doubles in about ____ years??
thank you

Solution

compound interest formula: A= Ao(1+r)^t, Ao = initial investment, r = interest rate per period, t = number of periods, A = amount after t periods.
For continuous compounding: A=Aoe^rt
..
Quarterly compounding: A/Ao = 2, r = 0.07/4 = 0.0175 t = quarters
2 = (1+0.0175)^t
2 = (1.015)^t
take log of both sides
log(2)=t log(1.0175)
t = log(2) / log(1.0175)
t = 39.95 qtrs or: 39.95 / 4 = 9.9875 years

Continuous compounding: A/Ao = 2, r = 0.07, t = years
A=Aoe^rt
2 = e^0.07t
ln2 = 0.07t
t = ln2/0.07
t = 9.9021 years

Hope this helps