SOLUTION: Im sorry I haven't taken a math class in 20 years and I wasn't good to begin with and so I am lost here. I don't want someone to answer for me, I just wanna know how to do it corre

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Question 878985: Im sorry I haven't taken a math class in 20 years and I wasn't good to begin with and so I am lost here. I don't want someone to answer for me, I just wanna know how to do it correctly.
How many years will it take $1000 to grow to 1700 if invested at 6 percent and compounded quarterly? continuously?
Thankyou
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
For the "compounded quarterly" part, use the formula FV+=+PV%2A%281%2Br%2Fn%29%5E%28n%2At%29

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%2A%281%2Br%2Fn%29%5E%28n%2At%29 Start with the given equation.

1700+=+1000%2A%281%2B0.06%2F4%29%5E%284%2At%29 Plug in the given info.

1700%2F1000+=+%281%2B0.06%2F4%29%5E%284%2At%29 Divide both sides by 1000.

17%2F10+=+%281%2B0.06%2F4%29%5E%284%2At%29 Reduce.

1.7+=+%281%2B0.06%2F4%29%5E%284%2At%29 Convert 17%2F10 to decimal form.

1.7+=+%281%2B0.015%29%5E%284%2At%29 Divide 0.06%2F4 to get 0.015

1.7+=+%281.015%29%5E%284%2At%29 Add.

log%28%281.7%29%29+=+log%28%28%281.015%29%5E%284%2At%29%29%29 Apply logs to both sides (so we can isolate that exponent)

log%28%281.7%29%29+=+4t%2Alog%28%281.015%29%29 Pull down the exponent (one of the many log rules).

log%28%281.7%29%29%2Flog%28%281.015%29%29+=+4t Divide both sides by log%28%281.015%29%29.

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

35.6398725055742%2F4+=+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.

-------------------------------------------------------

For the next part, the "compounded continuously" part, use the formula FV+=+PV%2Ae%5E%28r%2At%29

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.