Task $1.$ A customer in a bank withdrew PLN $10000$ from a savings account after $3$ years. The nominal interest rate was

$3\mathrm{.}5\%.$ The deposit lasted $3$ years. For the last $15$ months a simple interest rate method was used, before that for $9$ months

a compound interest rate, and at the beginning a continuous compounding interest rate $($after each change in the interest

rate method the profits were credited to the account balance$).$ Please calculate how much was saved at the beginning of

this deposit.

Task $2.$ Calculate the difference in the diminishing monthly payment for a TV worth PLN $3,500$ purchased for a loan if

the purchase commission of PLN $100+0\mathrm{.}8\%$ of the value of the goods is paid "out of pocket" at the beginning $($in

advance$)$ compared to the situation where the commission is included in the monthly payment $($a credited commission$).$

Assume there are $10$ instalments and the interest rate is $12\%($with monthly capitalisation$).$