Kate invests $500 at the beginning of each year for 12 years into a fund earning an effective annual interest rate of 5%. Interest is paid on the fund at the end of each year. Kate takes each interest payment and reinvests it in another fund earning a rate of 4%. Find the combined value of Kate's two funds at the end of year 12

$7,888.55

Explanation:

we can prepare Katie's expected balance on her accounts:

end of year 1 = $500 x (1 + 5%) = $525

end of year 2 = $525 + [$525 x (1 + 4%)] = $1,071

end of year 3 = $525 + [$1,071 x (1 + 4%)] = $1,638.84

end of year 4 = $525 + [$1,638.84 x (1 + 4%)] = $2,229.39

end of year 5 = $525 + [$2,229.39 x (1 + 4%)] = $2,843.57

end of year 6 = $525 + [$2,843.57 x (1 + 4%)] = $3,482.31

end of year 7 = $525 + [$3,482.31 x (1 + 4%)] = $4,146.60

end of year 8 = $525 + [$4,146.60 x (1 + 4%)] = $4,837.47

end of year 9 = $525 + [$4,837.47 x (1 + 4%)] = $5,555.97

end of year 10 = $525 + [$5,555.97 x (1 + 4%)] = $6,303.21

end of year 11 = $525 + [$6,303.21 x (1 + 4%)] = $7,080.33

end of year 12 = $525 + [$7,080.33 x (1 + 4%)] = $7,888.55