Mortgage refinancing

Six years ago, Ayra purchased a brand$-$new condominium in Edmonton for $$500,000.$ Ayra had been

saving for her first home purchase ever since she graduated from UTSC, and she was able to make the

$20\%$ required down payment to avoid mortgage loan insurance. At that time, the interest rate on a $10-$year

fixed rate mortgage loan was $7\mathrm{.}120\%$ and the rate on a $25-$year fixed rate mortgage loan was $9\mathrm{.}240\%.$ Ayra

decided to take on a $25-$year fixed rate mortgage loan. Please remember interest rate on mortgage loan is

always compounded semiannually.

Today, Ayra works at Bank of Edmonton $($BOE$)$ as a marketing manager. A couple of weeks ago during

lunch, she was having a conversation with some of her colleagues at the mortgage department. Mortgage

loan rates had fallen, and she was advised to see whether she could refinance her mortgage loan to save

some money. Normally, the penalty for refinancing a mortgage loan equals the amount of interest paid

over the past three months. However, as a BOE employee, Ayra does not have to pay the penalty.

Following are the fixed mortgage loan rates BOE is offering:

What would you advise her to do if she would consider refinancing her mortgage loan using a $10$year

fixed rate mortgage?