You plan to accumulate $100,000$ at then end of $42$ years. You make

the following deposits:

i$)$ X at the beginning of years $1-14.$

ii$)$ No deposits at the beginning of years $15-32.$

iii$)$ Y at the beginning of years $33-42.$

The annual effective interest rate is i $=7\%$ and X $$ Y $=100.$

Find Y $.$