Calculate the following:

Suppose you wish to raise some money for your favorite local charity. This charity needs $50,000 a year to run its operation and you want to make sure that it is ensured an annual payment of this amount from now on for every year in the foreseeable future. Given an interest rate of 5%, how much would you have to fund this perpetuity to guarantee the charity a payment of $50,000 per year?

You decide to put $1,000 in a new bank account and don’t plan to withdraw the money for 10 years. If your bank does continuous compounding and the interest rate is 1%, what will be the value of this bank account in 10 years?