You have $2000 to invest in an account and need to have $2500 in five years. what annual interest rate would you need to have in order to have this if the amount is compounded monthly?
a- 5%
b-2%
c-4%
d-3%

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) ] =

[ 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)

the first option is the answer.

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