Question #$1$

Answer the following questions assuming, where necessary, the interest rate is $10\%.$

$($i$)$ What is the present value of $$1,000$ in $8$ years? Why does the present value fall as the number of years increases?

$($ii$)$ How long will it take for a $$2,000$ investment to triple in value?

$($iii$)$ An investment of $$1,300$ today returns $$60,972$ in $50$ years. What is the rate of return on this investment?

Question #$2$

$($i$)$ What's the future value of $$2,000$ after $3$ years if the appropriate interest rate is $8\%$ per annum compounded monthly?

$($ii$)$ Suppose you invested $$1,000$ in stocks $10$ years ago. If your account is now worth $$2,839\mathrm{.}42,$ what rate of return did your stocks earn?

$($iii$)$ You are investing your money in a bank account with an interest rate of $8$ percent, compounded annually. If you invest $$2,000$ today, approximately how many years will it take for your account to grow to $$10,000?$

Question #$3$

Answer the following questions assuming, where necessary, the interest rate is $10\%.$

$($i$)$ A couple wishes to save $$250,000$ over the next $18$ years for their child's education. What annual amount must they deposit at the end of each year?

$($ii$)$ What return do you earn if you pay $$22,470$ for a stream of $$5,000$ payments lasting ten years? What does it mean if you pay less than $$22,470$ for the stream? More than $$22,470?$

$($iii$)$ A company is planning to set aside money to repay $$150$ million in bonds that will be coming due in $8$ years. How much money would the company need to set aside at the end of each year for the next $8$ years to repay the bonds when they come due? How would your answer change if the money were deposited at the beginning of each year?

Please solve and explain.