$0.$ What is the present value $($PV$)$ of $$100,000$ received five years from now, assuming

the interest rate is $8\%$ per year?

$51.$ What is the future value $($FV$)$ of $$60,000$ in five years, assuming the interest rate is $5\%$

per year?

$52.$ If the future value $($FV$)$ in two years of $$100,000$ invested in a certain fund that

compounds it at a fixed rate annually is $$116,640,$ at what rate has it been compounded?

$53.$ Sara wants to have $$500,000$ in her savings account when she retires. How much must

she put into the account now, if the account pays a fixed interest rate of $8\%,$ to ensure that

she has $$500,000$ in $20$ years$$ time?

$54.$ On the day Harry was born, his parents put $$1000$ into an investment account that

promises to pay a fixed interest rate of $4$ percent per year. How much money will Harry

have in this account when he turns $18?$

$55.$ Consider the following timeline:

If the current market rate of interest is $9\%,$ then the present value $($PV$)$ of this timeline as

of year $0$ is closest to what?

$56.$ Consider the following timeline: