+67 1. John invests \($4,200\) at an annually compounded interest rate of 6%. Josey invests \($4,200\) at a simple interest rate of r%. What is r if their investments are worth the same amount after 1 year? 2 years? 10 years?
2. Show that if \($k\) is invested at an interest rate of r% for n years, compounded annually, then the total amount at the end of n years is
\((1+\frac{r}{100})^n ($k)\)
3. Show that if \($k\) is invested at an interest rate of r% for n years, compounded m times a year, then the total amount at the end of n years is
\((1+\frac{r}{100m})^{nm} ($k)\)
4. Bobby takes a \($3,000\) loan that compounds semi-annually (twice a year). He makes no payments for the first 4 years, and after 4 years he owes \($3,950.43\). What is the interest rate of the loan?
5. How much money should Poppy invest at an annually compounded interest rate of 5% so that she has \($500,000\) in ten years?
6. The annually compounded interest rate for the next 20 years is 8%. You win a lottery and are allowed to choose one of the following four options. Order the options from most valuable to least valuable.
(a) Receive \($100,000\) in 20 years
(b) Receive \($50,000\) in 10 years
(c) Receive \($30,000\) in 10 years and another $$50,000$ in 20 years
(d) Receive \($25,000\) right away.
Thank you
