The formula can be used to find the number of years t required for an investment P

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The formula


imagecan be used to find the number of years t required for an investment P to grow to a value A when compounded continuously at an annual rate r.


(a) How long will it take to increase an initial investment of $1000 to $4500 at an annual rate of 5.75%?


(b) What annual rate is required to increase the value of a $2000 IRA to $30,000 in 35 years?


(c) Give a derivation of this formula.

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