Answer:
8.17 years(closest to 8 years )
Explanation:
The future value of $50,300, would be accumulated after 5 years of having made the investment(3 years+2 years=5 years)
As a result, we can determine the annual rate of return based on the future value in year 5 using the future value formula below:
FV=PV*(1+r)^n
FV=future value=$50,300
PV=amount invested initially=$32,200
r=unknown=annual rate of return
n=5 years
$50,300=$32,200*(1+r)^5
$50,300/$32,200=(1+r)^5
$50,300/$32,200 can be rewritten as ($50,300/$32,200)^1
($50,300/$32,200)^1=(1+r)^5
divide index on both sides by 5
($50,300/$32,200)^(1/5)=1+r
r=($50,300/$32,200)^(1/5)-1
r=9.33%
Our next task is to determine how long( in years) it takes to accumulate a future value of $87,200 from today's point, which means we need to determine the value of the investment today( 3 years after making the investment)
FV=$32,200*(1+9.33%)^3
FV=value of investment today=$42,079.82
Lastly, we can ascertain when $42,079.82 today would become $87,200
$87,200=$42,079.82*(1+9.33%)^n
n=number of years=unknown
$87,200/$42,079.82=(1+9.33%)^n
$87,200/$42,079.82=1.0933^n
take log of both sides
ln ($87,200/$42,079.82)=n ln(1.0933)
n=ln ($87,200/$42,079.82)/ln(1.0933)
n=0.72863604/0.08920065
n=8.17 years( from today, approx 8 years)
