SOLUTION: If $ 110000 is to grow to $ 250000 in ten years period, at what annual interest rate must it be invested, given that interest is compounded semi annually ?

Algebra ->  Finance -> SOLUTION: If $ 110000 is to grow to $ 250000 in ten years period, at what annual interest rate must it be invested, given that interest is compounded semi annually ?      Log On


   

Question 980996: If $ 110000 is to grow to $ 250000 in ten years period, at what annual interest rate must it be invested, given that interest is compounded semi annually ?
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
That is two compoundings per year for ten years, making twenty compounding periods.

110000%2A%281%2Br%2F2%29%5E20=250000, the growth equation with the values filled; only interest rate r, is unknown; r is a decimal value, a fraction. You could also treat the binomial as a variable, if this is easier.

%281%2Br%29%5E20=25%2F11

log%2810%2C%281%2Br%29%5E20%29=log%2810%2C%2825%2F11%29%29

20%2Alog%2810%2C%281%2Br%29%29=log%2810%2C%2825%2F11%29%29

log%2810%2C%281%2Br%29%29=%281%2F20%29log%2810%2C%2825%2F11%29%29

Evaluate or compute the righthand member.

log%2810%2C%281%2Br%29%29=0.0178273661756906284411161119654, far more accuracy than meaningful.

Antilog of 0.0178273661756906284411161119654 will be 1+r.
... 1%2Br=1.0419
For ONE compounding period, rate is 4.19%, so for a whole year, 8.38%.