If Tanisha has $1000 to invest at 9% per annum compounded semiannually, how long will it be before she has $1700?
Answer (2)
Use the compounding formula
FV = PV (1+i)^n i = decimal interest per period = .09/2
n = periods ( each period is 1/2 year ) = ?
FV = $1700
1700 = 1000 ( 1+ .09/2)^n
1.7 = 1.045^n LOG both sides
log ( 1.7) = n log (1.045)
n = log(1.7)/log(1.045) = 12 periods (two periods per year) ** which is 6 years** ;
Tanisha's investment of $1000 at 9% compounded semiannually will take approximately 6.12 years to grow to $1700. This is calculated using the compound interest formula and isolating the variable for the number of compounding periods. The answer is derived by using logarithms to solve for the time.
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