SOLUTION: How many years will it take $5,000 to grow to $7,500 if it is invested at 8% compounded semiannually? Compounded continously?

Question 16752: How many years will it take $5,000 to grow to $7,500 if it is invested at 8% compounded semiannually?
Compounded continously?
Answer by bam878s(77) (Show Source): You can put this solution on YOUR website!
we are given annual interest rate i = 8% or .08
the semiannual interest rate is then = = .04
the per period accumulation function is then
so, we have 7500 = 5000 * . First divide 5000 from both sides.
1.5 =
log 1.5 = n log 1.04
divide log 1.04 from both sides
n = 10.3380351 half years or 5.1690175 years.
For continous interest we need to find the force of interest (d) over the accumulation period.
we know =
so =
n ln 1.08 = nd (take the natural log of both sides)
ln 1.08 = d
now the accumulation function for continuous interest is
so 5000 * = 7500
= 1.5
= ln 1.5 (take the natural log of both sides)
n =
n = 5.2684462
Hope this helps, let me know if you have any more financial mathematics questions. I know them fairly well.
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