Word problem sum of geometric series

Question

Michael is saving 400 dollars a month towards retirement in an account that earns 4% annual interest. Michael plans on saving this for 10 years (120 months). How much money will he have saved? (Using the formula for the sum of geometric series to find the sum of the series)

Answer 1

$58,899.92 rounded down to nearest penny

sn = a1(1-r^n)/(1-r)

a1 = 400=1st term, n=120=number of terms, r =1+,04/12= common ratio

plug in the values to find sn=sum of the geometric series =58899.92192=about 58899.92

or another formula:

FV = PMT x (1+i^n) -1)/I I = monthly interest rate = r/12 = .04/12=.01/3 PMT =400, n=120

= 400x (1+ (1/300)^120) -1)/(1/300)

= 58899.92

which includes principal plus interest compounded monthly

400x120=48000 = all the payments

interest = 10,899.92