SOLUTION: how long, to the nearest year, will an investor have to invest R 20 000 to grow to R24 000, if the interest rate is 6% per year and the interest is compounded every 6 months??

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Question 986186: how long, to the nearest year, will an investor have to invest R 20 000 to grow to R24 000, if the interest rate is 6% per year and the interest is compounded every 6 months??
Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
Using time increments of every six months is the easiest way to do.

20000%281.06%29%5Ex=24000
x is the number of compounding periods and you are given than x=1 means %281%2F2%29year.

20%281.06%29%5Ex=24
5%281.06%29%5Ex=6
log%2810%2C%285%2A1.06%5Ex%29%29=log%2810%2C6%29
log%2810%2C5%29%2Bx%2Alog%2810%2C1.06%29=log%2810%2C6%29
x%2Alog%2810%2C1.06%29=log%2810%2C6%29-log%2810%2C5%29
highlight_green%28x=log%2810%2C%286%2F5%29%29%2Flog%2810%2C1.06%29%29

x=3.128968 compounding periods, but we cannot really use that much accuracy. Try knocking down to the nearest month or nearest week.

3.128968%286%29%2Amonths
or
18.77 months
or
18 months 23 days

If you just want YEARS, then 18.77%2Amonths%281%2F12%29%28years%2Fmonth%29=1.564+years.