Question $3.(6$ pts$)$ If Jonathan instead wants to deposit a small amount d to the Husky

Bank Inc. each period of compounding and still wants to get $$150,000$ after $5$ years, how

much should d be$,$ if the annual interest rate is $3\mathrm{.}6\%,$ and the interest is calculated

$($a$)$ annually?

$($b$)$ monthly?

Question $4.(6$ pts$)$ If Jonathan decides to directly take a loan of $$150,000$ from the bank

with the annual interest rate $3\mathrm{.}6\%$ and pay it back later.

$($a$)$ How much is the monthly payment that Jonathan needs to make so that he can pay off

the loan after $10$ years?

$($b$)$ Given the monthly payment in part $($a$),$ how much does Jonathan still owe the bank

after $5$ years?

Question $5.$ In this question, we consider the compound interest for Jonathan: the

principal is $$50,000$ and the annual rate is $3\mathrm{.}6\%,$ compounded monthly.

$($a$)(1$ pt$)$ How many months does it take Jonathan to have enough $$150,000?$

$($b$)*(1$ bonus pt$)$ Suppose now the time t is $10$ years. What will happen to the end amount

at the end $10$ years, if the number of compounding periods per year $($the term k in the

formula$)$ tends to infinity? Explain your answer.

$($Hint: the end amount will not tend to infinity$).$