0
Want this question answered?
Be notified when an answer is posted
Add your answer:
Earn +20 pts
How many years will it take to save 200000 if you place 1700 per month in an account that earns 7 percent compounded monthly?
I get seven and a half years (90 months). If you have a spread sheet (or calculator) you can use the following formula for finding the amount accumulated "Pn" after "n" months at monthly compounded interest "i" and monthly savings "d" Pn = (d/i)[(1+i)^(n+1) - 1] the monthly interest rate is found from the annual rate "I" from ; i = (I+1)^(1/12) - 1. Using I = .07 (7%) , this gives i = .00565. In the Pn equation you can solve for any other variable you choose. However solving for "n" , which is really what you asked for, involves logarithims and with a spread sheet its easier to just try different "n's" and see what gets you $200,000 for "Pn". Using this approach I got n = 90 months will get you about $201,000. ------------------------------------------------------------ The previous answer is a good attempt at approaching the question intuitively. However, this question, though cryptically so, is a geometric series question. Consider the following: Let's say the person deposits 1700 at the beginning of the first month. After one month, the amount would be 1700*(1+0.07/12). At this point, the person deposits another 1700. One month after that, the first 1700 would gain two months' interest and become 1700*(1+0.07/12)2 and the 1700 deposited in the second month would accumulate one month's interest and become 1700*(1+0.07/12). The person deposits another 1700. Therefore, the following list represents the total amount of money the person will have: End of first month: 1700*(1+0.07/12) + 1700 End of second month: 1700*(1+0.07/12)2 + 1700*(1+0.07/12) + 1700 End of third month: 1700*(1+0.07/12)3 + 1700*(1+0.07/12)2 + 1700*(1+0.07/12) + 1700 ...... End of nth month: 1700*(1+0.07/12)n + 1700*(1+0.07/12)(n-1) + ... + 1700*(1+0.07/12)2 + 1700*(1+0.07/12) + 1700 Let's say that after nth month, the total amount is 200000 Now we recognize the formulat for the total amount of money at the end of the nth month is a geometric series with a = 1700 and r = (1+0.07/12) and n = n. Therefore: 200000 = 1700*(1+0.07/12)n + 1700*(1+0.07/12)(n-1) + ... + 1700*(1+0.07/12)2 + 1700*(1+0.07/12) + 1700 200000 = a(1-rn)/(1-r) 200000 = 1700(1-(1+0.07/12)n)/(1-(1+0.07/12)) n = log(1-200000*(-0.07/12)/1700)/log(1+0.07/12) n = 89.836 n ~ 90 months Additional Comments I would like to make two comments. First, regarding the second answer. Although .07/12 is approximately the monthly interest it does not give the correct value of 7% per annum because of the monthly compounding. Second, regarding the first answer. It is not an "intuitive" result. The equation for "Pn" is a rigorous derivation based on the same geometrical series analysis in the second solution. My intent was to spare the questioner the lengthy analysis required to arrive at the solution.
WHAT IS 15 OF 1700?
1700/100*15=255
What is 1723 rounded to the nearest 100?
1700
What is 1659 rounded to the nearest hundred?
1700
What does MDCC mean in roman Numerals?
MDCC = 1700
About how far did Coronado and his group travel?
Coronado and his group crossed the Colorado river and explored what is now the southwestern United States. He reached what is now New Mexico.
Who was the first person to group organisms?
In the mid 1700's Carolus Linnaeus began to organize and group organisms.
What are the IR frequencies of an aldehyde carbonyl group?
around 1700 cm^(-1)
Where is a carbonyl group detected by FTIR?
At around 1700-1800 [1/cm]
The mission founded in Texas during the 1700 are evidence of the cultural influence of which group?
spanish
What year was the 17 century AD?
From 1601 to 1700.From 1601 to 1700.From 1601 to 1700.From 1601 to 1700.From 1601 to 1700.From 1601 to 1700.From 1601 to 1700.From 1601 to 1700.From 1601 to 1700.From 1601 to 1700.From 1601 to 1700.
Iraq's second largest group?
Kurds is the second largest group in Iraq.
The second group of three rulers of rome was?
There was no second group of three rulers in Rome.
What is a latter group?
a later group. latter by definition means later or after, or second. so once you figure it out latter group= later or second group
How fast is 1700 feet per second?
That s about 1160 mph, faster than the speed of sound
A group of thinkers in the 1700's who believed in reason liberty natural law progress and human happiness?
This group of thinkers is known as the Enlightenment thinkers or philosophers. They believed in using reason and logic to challenge traditional beliefs, promote individual liberties, advocate for natural laws governing society, and work towards the progress and improvement of human happiness through education and rational thought. Key figures include Voltaire, Rousseau, Montesquieu, and Locke.
What is the second most important mineral group?
Carbonates are the second most important mineral group.
