$1.$John, a college student needs to borrow $$5,000$ today for his tuition bill. He agrees to pay back the loan in a lump$-$sum payment five years from now, after he is out of college. The bank states that the payment will need to be $$7,012\mathrm{.}76.$ If John borrows the $$5,000$ from the bank, what interest rate is he paying on the loan?

$\mathrm{.}2.$Happy Harry has just bought a scratch lottery ticket and won $$10,000.$ He wants to finance the future study of his newly born daughter and invests this money in a fund with a maturity of $18$ years offering a promising yearly return of $6\%.$ What is the amount available on the $18$th birthday of his daughter?

$3.$Ruby will retire in $20$ years. This year he wants to fund an amount of $$15,000$ to become available in $20$ years. How much does he have to deposit into a pension plan earning $7\%$ annually?

$4.$Peter will invest $$5,000$ in $2$ years and $x$ in $4$ years' time. The present value of those investments is $10,000.$ The interest rate is $5\%.$ Calculate the value of $x?$