Question

A person saves $100 in month 1, $105 in month 2, with increasing monthly amounts by $5 through year five. Assuming 6% interest annually, monthly compounding, what is the value of this account at the end of five years?

Answer 1

i = 6%/12 = 0.5% per month

t = 5*12 = 60 months

FW after 5 yrs = 100*(F/A,0.5%,60) + 5*(F/G,0.5%,60)

= 100*(((1 + 0.005)^60-1)/0.005) + 5*{((1 + 0.005)^60-1)/(0.005^2) - 60/0.005}

= 100*(((1.005)^60-1)/0.005) + 5*{((1.005)^60-1)/(0.005^2) - 60/0.005}

= 100*69.770031 + 5*1954.0061

= 16747.03