Question 1189903: If money is invested at r percent interest, compounded annually, the amount of the investment will double in approximately 70/r years. If Pat's parents invested $5,000 in a long-term bond that pays 8 percent interest, compounded annually, that will be the approximate total amount of the investment 18 years later, when Pat is ready for college?
A. $20,000 B. $15,000 C. $12,000 D. $10,000 E. $9,000
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! at 8% interest, compounded annually, the money will double in 9.006468342 years.
the formula is:
2 = 1.08 ^ n
take the log of both sides of the equation to get:
log(2) = n * log(1.08)
solve for n to get:
n = log(2) / log(1.08) = 9.006468342.
you stated that the money will double in approximately 70/r years.
the r in your statement would have to be 8 percent, not .08.
70/8 = 8.75.
that's pretty close, but not right on, and lower than what the doubling number of years is.
5000 invested at 8% for 18 years would be equal to 5000 * 1.08 ^ 18 = 19980.0975.
the formula uses the rate, not the percent.
the growth factor is 1 plus the rate = 1.08.
let me know if this satisfies your inquiry.
if not, let me know, in more detail, what it is that you're looking for that i'm missing.
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