Step $1$: Calculate Future Value of the First $4$ Years of DepositsFirst, we need to calculate the future value of the monthly deposits for the first $4$ years. We'll use the formula for the future value of an annuity:FV$=$P$\backslash$times $($ r$(1+$r$)$ n $1)$Where:P is the monthly depositr is the monthly interest raten is the number of periodsFor the first $4$ years:P$=$$$150$r$=44\%=1\%=0\mathrm{.}01($quarterly interest rate$)$n$=4\backslash$times $12=48(48$ months$)$FV $1=150\backslash$times $(0\mathrm{.}01(1+0\mathrm{.}01)481)$Step $2$: Calculate Future Value of the Next $2$ Years of DepositsNext, we calculate the future value of the increased monthly deposits for the next $2$ years. We'll use the same formula, but with different values:P$=$$$250$r$=0\mathrm{.}01($quarterly interest rate$)$n$=2\backslash$times $12=24(24$ months$)$FV $2=250\backslash$times $(0\mathrm{.}01(1+0\mathrm{.}01)241)$Step $3$: Calculate the Total Future ValueFinally, we add the future values of the two periods to get the total future value:FV total $=$FV $1+$FV $2$ Let's calculate these values.CalculationsStep $1$: Calculate Future Value of the First $4$ Years of DepositsFV $1=150\backslash$times $(0\mathrm{.}01(1+0\mathrm{.}01)481)$FV $1=150\backslash$times $(0\mathrm{.}01(1\mathrm{.}01)481)$FV $1=150\backslash$times $(0\mathrm{.}011\mathrm{.}6084371)$FV $1=150\backslash$times $(0\mathrm{.}010\mathrm{.}608437)$FV $1=150\backslash$times $60\mathrm{.}8437$FV $1=9026\mathrm{.}555$Step $2$: Calculate Future Value of the Next $2$ Years of DepositsFV $2=250\backslash$times $(0\mathrm{.}01(1+0\mathrm{.}01)241)$FV $2=250\backslash$times $(0\mathrm{.}01(1\mathrm{.}01)241)$FV $2=250\backslash$times $(0\mathrm{.}011\mathrm{.}2682411)$FV $2=250\backslash$times $(0\mathrm{.}010\mathrm{.}268241)$FV $2=250\backslash$times $26\mathrm{.}8241$FV $2=6710\mathrm{.}2525$Step $3$: Calculate the Total Future ValueFV total $=$FV $1+$FV $2$ FV total $=9026\mathrm{.}555+6710\mathrm{.}2525$FV total $=15736\mathrm{.}8075$So$,$ by the end of the $6-$year period, Amir will have saved approximately $$15,736\mathrm{.}81.$### ConclusionAmir will have saved approximately$$15,736\mathrm{.}81$ by the end of the $6-$year period, considering his monthly deposits and the interest earned on those deposits.