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## 15-year loan - savings over the life of the loan

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!

THE SCENARIO When I get ads from my lender about refinancing, they typically include a 15-year option, which has a (slightly) lower interest rate, and which 'can save [me] thousands over the life of the loan!' The question: How much money would I save over the life of the loan if I were to borrow \$300,000 for 15 years at 4.375% instead of for 30 years at 4.625%? Both loans amortize fully.
THE SOLUTION To solve this one, we need to do three things:
1. Figure out the total of all payments for the 15 year loan
2. Figure out the total of all payments for the 30 year loan
3. Subtract the two to find the savings
First things first, make sure the calculator is using 12 Payments per Year. Part 1: The 15-year loan N: 180 (15 years is 180 months) I/YR: 4.375 (The 15 year loan is at 4.375%) PV: 300,000 (I'm borrowing \$300,000) PMT: (This is what I'm trying to find) FV: 0 (The loan amortizes fully) When I solve for PMT, I get that my monthly payment will be \$2,275.86 for this loan.

The total of all payments in the 15-year loan is 180 x \$2,275.86 = \$409,654.80*.

Part 2: The 30-year loan N: 360 (30 years is 360 months) I/YR: 4.625 (The 30 year loan is at 4.625%) PV: 300,000 (I'm borrowing \$300,000) PMT: (This is what I'm trying to find) FV: 0 (The loan amortizes fully) When I solve for PMT, I get that my monthly payment will be \$1,542.42 for this loan.

The total of all payments in the 30-year loan is 360 x \$1542.42 = \$555,271.20*.

Part 3: The savings

If I get the 15-year loan instead of the 30-year loan, I pay the bank \$555,271.20 - \$409,654.80 = \$145,616.40 less overall.

Okay, so if I go for the shorter loan, then I can pay \$145k less interest - and given that the 15-year loan only has \$110k in interest overall, that's pretty significant. So why would I want to take the 30-year loan instead of the 15-year loan? Can you think of any reason that might be more compelling to me than the monetary savings? Or do you have a strong preference for the 15-year option for any reason other than paying less interest? Let us know in the comments!

* Remember that when multiplying your payment amount by the number of payments, you have to use whole pennies. When you calculate PMT, the calculator will figure out the answer to 10 or more decimal places, but you can only pay in whole pennies, so you have to re-enter the rounded PMT number the calculator gives you before multiplying by the number of payments. If you don't, then when you multiply by 180 or 360, your answer may be off by a few cents. Not the end of the world, but if your answer differs from mine, that's probably why.