s$.$ Lucy inherited a large sum of money from her aunt. She invested part of her inher$-$

itance into a fund earning $6\%$ compounded monthly. She has arranged a systematic

withdrawal plan that provides for $120$ monthly payments increasing at a constant

rate of$0\mathrm{.}5\%$ per paym ent. The first paym ent of $$400$ is due one month after she set

up the fund. H ow m uch interest is included in the payments?