Answer:
r = 4.47% (= 4% when rounded to nearest whole number)
Step-by-step explanation:
Recall that the formula for compound interest is:
A=P [ 1+(r/n) ]^(nt)
Where
A = Final Amount = $2500
P = Principal amount = $2000
r = interest rate (we are asked to find)
n = number of times compounded in a year. In our case it is compounded monthly (i.e 12 times a year) hence n = 12
t = time = 5 years
Substituting this into the formula:
2500=2000 [ 1+(r/12) ]^(12x5)
2500=2000 [ 1+(r/12) ]^(60) (evaluate power and rearrange)
[ 1+(r/12) ]^(60) = 2500/2000
[ 1+(r/12) ]^(60) = 1.25 (taking 60th root on both sides)
[ 1+(r/12) ] = [tex]\sqrt[60]{1.25}[/tex]
[ 1+(r/12) ] = 1.003726 (subtract 1 from both sides)
r/12 = 0.003726 (multiply both sides by 12)
r = 0.003726 x 12
r = 0.0447
r = 4.47% (= 4% when rounded to nearest whole number)
