$($Related to Checkpoint $5\mathrm{.}6)($Solving for i$)$ Springfield Learning sold zero coupon bonds $($bonds that don't pay any interest, instead the bondholder gets just one payment, coming when the the issuer$)$ and received $$800$ for each bond that will pay $$20,000$ when it matures in $40$ years.

a$.$ At what rate is Springfield Learning borrowing the money from investors?

b$.$ If Nancy Muntz purchased a bond at the offering for $$800$ and sold it $20$ years later for the market price of $$3,300,$ what annual rate of retum did she earn?

c$.$ If Barney Gumble purchased Muntz's bond at the market price $($$$3,300)$ and held it $20$ years until maturity, what annual rate of return would he have earned?

a$.$ At what rate is Springfield Learning borrowing the money from investors?

$8.38\%($Round to two decimal places$)$

b$.$ If Nancy Muntz purchased a bond at the offering for $$800$ and sold it $20$ years later for the market price of $F{V}_n,$ what annual rate of return did she earn?

$($Round to two decimal places $)$