http://www.ajdesigner.com/phpdiscountfac...
In your case each period n is 3 months and the 6.5% interest rate is the APR so you earn i= 6.5/4 % each quarter. The equation uses the decimal equivalent of the quarterly interest rate. Make a graph of n vs money to find when the graph crosses 1 million dollars.
"... $155,000 from the estate of a long-lost rich uncle. If you invest all your inheritance in a tax-free bond fund earning 6.5% compounded quarterly..."
FV / PV = call this M for Multiple
1,000,000 / 155,000 = 6.45161
r = 0.065 /4 = 0.01625
t = ln(M) / ln(1 + r)
t = ln(6.45161) / ln(1.01625)
t = 1.86433 / 0.01612
t = 115.65767...since you used a quarterly rate (quarterly compounding), this "t" reflects the number of quarters it takes to multiply your money 6.45161 times. (e.g. 155,000 x 6.45161 = 1,000,000. Note that my calculator "remembers" all the places after the decimal point, so simply plugging in 6.45161 will not actually result in $1m. The "real" M is 6.45161290 etc.)
convert "t" : quarters into years by dividing by 4
115.65767 / 4 = 28.91442 years, or 28 years and (12 x 0.91442 = ) 10.97 months, round to 28 years, 11 months.
The name of the link in sources is a bit misleading. It will show you how to calculate time to double: t = ln(2) / ln(1 + r)
notice that M = 2, as in doubling
you can use this formula with any Multiple
I have been stuck on this problem for quite some time. There are a few more problems like this, so I appreciate if whoever can help me also provides the equation used to solve this problem. Thank you!! :-)
You have just received $155,000 from the estate of a long-lost rich uncle. If you invest all your inheritance in a tax-free bond fund earning 6.5% compounded quarterly, how long do you have to wait to become a millionaire? (Round your answer to two decimal places.)
