Question 878985
For the "compounded quarterly" part, use the formula {{{FV = PV*(1+r/n)^(n*t)}}}


where,


FV = future value (amount you will have in the account at some point in the future)
PV = present value
r = interest rate (in decimal form)
n = compounding frequency
t = time in years


In this case,


FV = 1700 (amount you want t years in the future)
PV = 1000 (amount you deposit right now)
r = 0.06 (6% = 6/100 = 0.06)
n = 4 (compounded quarterly means you are compounding 4 times a year)
t = unknown (you are solving for this) 


Plug all of that info into the equation and solve for t


{{{FV = PV*(1+r/n)^(n*t)}}} Start with the given equation.


{{{1700 = 1000*(1+0.06/4)^(4*t)}}} Plug in the given info.


{{{1700/1000 = (1+0.06/4)^(4*t)}}} Divide both sides by 1000.


{{{17/10 = (1+0.06/4)^(4*t)}}} Reduce.


{{{1.7 = (1+0.06/4)^(4*t)}}} Convert {{{17/10}}} to decimal form.


{{{1.7 = (1+0.015)^(4*t)}}} Divide {{{0.06/4}}} to get {{{0.015}}}


{{{1.7 = (1.015)^(4*t)}}} Add.


{{{log((1.7)) = log(((1.015)^(4*t)))}}} Apply logs to both sides (so we can isolate that exponent)


{{{log((1.7)) = 4t*log((1.015))}}} Pull down the exponent (one of the many log rules).


{{{log((1.7))/log((1.015)) = 4t}}} Divide both sides by {{{log((1.015))}}}.


{{{35.6398725055742 = 4t}}} Use a calculator to evaluate the left side.


{{{35.6398725055742/4 = t}}} Divide both sides by 4.


{{{8.90996812639356 = t}}} Divide.


{{{t = 8.90996812639356}}} Flip the equation.


So it takes approximately 8.90996812639356 years. If you must round to a whole number, then round up to get 9 years. You round up to guarantee you let enough time go by to get past the target you want.


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For the next part, the "compounded continuously" part, use the formula {{{FV = PV*e^(r*t)}}}


where,


FV = future value (amount you will have in the account at some point in the future)
PV = present value
e = 2.718... (it's a constant like {{{pi}}} and it goes on forever without a known pattern)
r = interest rate (in decimal form)
t = time in years


I'll let you do this part.