Lenny D. answered • 01/19/20
Financial Professional with many years of Wall Street Experience
I will assume the interest accrues Daily and Compounds annually.
The First pass approach FV=PV(1+i)T
PV= 6390 FV= 20,751.53 so FV/PV=(20,751.53/6390)=(1+7.75%)T
Ln(FV/PV) =Tln(1.0775) or 1.17789=Tln(1.0775)=T(.07464) or T=1.17789/.07464 = 15.78 years. .78 years = .78*365 days 284 .75 days or roughly 6pm in the evening on the 285th day. However, this is only an approximation. It would be assuming the interest that has been accruing since the last compound date has been accruing. Simple interest will actually speed up the process a bit. This is why credit card companies use simple interest. If you pay in the middle of the month your interest charge will be higher.
\In this example we want to know how many days past 15 years it will take to get to 20751.53. Well 6390 compounding at 7.75% for 15 years would be worth 19,577.626 ( 6390*(1.0775)15 ) The difference 20,751.53 -19,577.626 = $1,173.90 is how much interest we have to accrue . Sooooooo. the daily amount of interest earned is (0775/365)*19,577.626 = 4.15689 dollars per day. How many days will it take, earning 4.15689 dollars per day to have 1,173.90 well, 1,173.9/4.15689 = 282.398 or roughly 9:55 am on the 283rd day of the year of the 16th year since the investment was made.
If you have any questions, please feel free to reach out. I have been doing this stuff far longer than I care to admit. and used to teach it to new hires at the big banks on Wall Street.
Lenny D.
ln is natural logarithm and Tln is T years Times The Natural logarithm01/19/20
Lenny D.
for example ln(2^4) = 4ln(2) l ln(X)^T =T*ln(X) etc..01/19/20
Megan B.
is there a way to answer the question without using Ln and TIn?01/19/20
Lenny D.
What you would have to do is take a guess at the number of years. Suppose that you guessed 10 years are you calculated how much there would be and you see it's not enough and then you guess 20 years if you said nope that's too much and you keep going back and forth until you figure out the number of years. Once you have the number of years then it's a matter of figuring the number of days most financial calculators will have a natural logarithm function and you can probably find a natural logarithm table as well. There's also a command in Microsoft Excel if you use that which is=ln()01/20/20
Lenny D.
Anytime that you need to figure out in amount of time in one of these compounding problems the fastest and surest way is to use natural logarithms01/20/20
Megan B.
Thank you so much, this helped a lot01/20/20
Lenny D.
That is great. If you need help please don't hesitate to book a session as I've only been doing this for a very long time01/20/20
Megan B.
Thank you so much, just wondering what "Ln" and "Tin" stands for01/19/20