$6$c$.$ Monthly Payment $--$ Show your work

Berdine and Beau Bourgeois have found a house they want to buy. They will need to borrow $$225,000$ and are now shopping around for a loan. Beau found a $30-$year loan at $6\mathrm{.}75\%,$ but thinks he can do better. By how much would their monthly payment drop if they could find a loan at a rate that is one$-$half percentage lower?

Payment at outstanding $6\mathrm{.}75\%$ rate

$\backslash$table$[[N=,],[\frac{i}{y}=,],[PV=,],[PMT=,],[FV=,]]$

What is the new rate?

$q,$

Payment with lower rate

$\backslash$table$[[N=,],[\frac{i}{y}=,],[PV=,],[PMT=,],[FV=,]]$

Show work here.

Answer: $q,$

$6$d$.$ Solve for $i--$ Show your work

Find the APR on a $$165,000$ loan which is amortized over $30$ years with a monthly payment of $$1,042\mathrm{.}91.$ Round to the nearest $10$ th of a percent.

Note: $\frac{i}{y}$ represents the rate per period $($which in this case is monthly$).$ However, since an annual rate is called for, the monthly rate must be converted to the equivalent annual rate.

$\backslash$table$[[N=,],[\frac{i}{y}=,],[PV=,],[PMT=,],[FV=,]]$

What did you calculate for $\frac{i}{y}?$ Annual Rate:

$\%$

$\%$

$($Please show $5$ decimal places for i$/$y result and nearest tenth percent

fnr annualized rate. $1q,$