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## What An Incredible Offer!

Note: You can use any financial calculator to do this problem, but if you want the BEST, you can get our 10bii Financial Calculator for iOS, Android, Mac, and Windows!
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THE SCENARIO I recently got a letter from a lender, offering an "incredible" loan-refinance offer. Reading the details, I was floored, and soon you'll understand why. The offer was to roll my recent balance of \$320,447 into a new 30-year loan at a 4.875% interest rate. The 30-year loan this would replace started 6 years and 9 months ago, had an initial balance of \$374,205, and an interest rate of 3.5%. The question: If I take them up on their amazing refinance offer, and there are no costs to doing the refinance*, how much money will I save over the life of the new loan versus my current loan? * Note: This pretty much never happens.
THE SOLUTION This one has several parts, but each of them is pretty straightforward.
1. Find the monthly payment for the new loan
2. Find the monthly payment for my current loan
3. Find the total payments over the life of the new loan
4. Find the total payments over the remaining life of my current loan
5. Find out the amazing savings this offer represents!
First things first, make sure the calculator is using 12 Payments per Year. Step 1: New loan's payment N: 360 (The new loan is a 30-year loan, which lasts for 30 x 12 = 360 months) I/YR: 4.875 (The new loan's rate is 4.875%) PV: 320,447 (The lender wants to lend me \$320,447) PMT: (This is what I'm trying to find) FV: 0 (The new loan amortizes fully)

The new loan's monthly payment would be \$1695.83.

Step 2: Current loan's payment N: 360 (My current loan is a 30-year loan, which lasts for 30 x 12 = 360 months) I/YR: 3.5 (My existing rate is 3.5%) PV: 374,205 (My current lender originally loaned me \$374,205) PMT: (This is what I'm trying to find) FV: 0 (The new loan amortizes fully)

The monthly payment on the current loan is \$1680.35.

Step 3: Total payments for new loan The new loan has 360 payments yet to be paid, each being \$1,695.83. The total I'd pay on the new loan would be 360 x \$1,695.83 = 610,499.48. Step 4: Total payments for existing loan The new loan started with 360 payments yet to be paid, but that was 6 years and 9 months ago. 6 years is 6 x 12 = 72 months. 72 months + 9 months = 81 months elapsed. So my current loan only has 360 - 81 = 279 months left to go. The total I'd pay on my current loan (if I kept it instead of refinancing) would be 279 x \$1,680.35 = 468,817.00. Step 5: Calculate "incredible" savings! If I were to refinance, I'd save an "incredible" \$468,817.00 - \$610,499.48 = negative \$141,682.48. That's right, not only would I have to pay more every month, but I'd be done in 30 years instead of 23, meaning that the refinance, on top of costing me money on a monthly basis, would also cost me an extra \$141,682.48 over the life of the loan. It's tempting, but I think I'm going to have to pass on this one.

What do you think? Am I missing something here? Have you gotten similar offers in the mail, and if so, were any of them actually worth doing? Let us know in the comments!