Another week, another TVM scenario for you!
This week we're going to refinance our home mortgage to lower our monthly payment!
Before we begin, please do me a favor! I've been told that these articles are too long and I should do a maximum of one or two problems in each, rather than five or so. Please leave me a comment letting me know if you think the articles you've seen so far are too long, too short, or a good length.
THE SCENARIO:
Building off of what we did last week, the situation is this:
I put $100,000 down and borrowed $350,000 to buy a house 34 months ago. The mortgage amortizes fully over 30 years, has monthly payments of $2,241.09,and the rate is 6.625%. I still owe $338,465.83, and thanks to a generous inheritance from my late Aunt Matilda, I have $100,000 to use to help me with my mortgage.
I figure that I'm more likely to be able to keep my house long-term if I have an easier time making those monthly payments. I've heard on the radio that interest rates are at all-time lows, and I've spent the last 3 years improving my credit score (which can help me to get the best rates), so I look up a mortgage broker to see if they can help me lower my payments. They give me a number of different options, and I want to find out what my payment is under each of them, and how much more or less I'll pay with a new loan than I do with my current loan.
Here are the options the loan broker laid out for me:
a) It'll cost me $10,000 in fees to do the refinance, and my new rate will be 3.625% for 30 years, amortizing fully.
b) It'll cost me $16,500 in fees to do the refinance, and my new rate will be 3.125% for 30 years, amortizing fully.
c) Refinancing will befree due to what he calls a 'Yield Spread Premium', and my new rate will be 4.875% for 30 years, amortizing fully.
d) It'll cost me $7,500 in fees to do the refinance, and my new rate will be 2.75% for 15 years, amortizing fully.
For each option, I'll pay the refinance fees out of the $100k and use the rest to paydown the current balance.
e) If I wanted to cut my payment to $800 per month and get a 40-year fully amortizing mortgage, what would my interest rate have to be?(Assuming the refinance cost me nothing in fees)
THE SOLUTION:
This is really five separate TVM (time-value of money) problems, and each is pretty straightforward. We'll set them up, one at a time.
a) N is 360, I/YR is 3.625, PV is$248,465.83, and FV is 0. Solving for PMT, I find that my new payment is $1,133.13, for a savings of $1,107.96. I nearly cut my payment in half - not bad!
b) N is 360, I/YR is 3.125, PV is $254,965.83, and FV is 0. Solving for PMT, I find that my new payment is $1,092.21, for a savings of $1,148.88. I paid more to do the refinance, so I start out owing more money on my new loan, but my payment went down by more than in scenario a). Interesting.
c) N is 360, I/YR is 4.875, PV is $238,465.83, and FV is 0. I solve for PMT, finding that my new payment is $1,261.98, for a savings of $979.11. Does it seem weird that in scenario b), I pay around a sixth of my inheritance on the refinance, but the payment ends up a lot lower than in scenario c), in which I put every dime I inherited into principal paydown.
d) N is 180, I/YR is 2.75, PV is $245,965.83, and FV is 0. I solve for PMT, and find that my new payment is $1,669.18, for a savings of $571.91. My savings is much lower in this scenario than in scenario b), but my debt is paid down in half the time. Would you find that tradeoff appealing?
To summarize the above:
| N | I/YR | PV (amount of new loan) | PMT (My new payment) |
|---|---|---|---|
| 360 | 3.625% | $248.5K ($248,465.83) | $1,133.13 |
| 360 | 3.125% | $255K($254,965.83) | $1,092.21 |
| 360 | 4.875% | $238.5K ($238,465.83) | $1,261.98 |
| 180 | 2.75% | $246K($245,965.83) | $1,669.18 |
e) N is 480, PV is $238,465.83, PMT is $800, and FV is 0. I solve for I/YR, and find that in order to get my desired payment, I need my rate to be no higher than 2.60%. That rate seems unlikely to be available (rates for longer loans tend to be higher than for shorter loans), so if I feel like I really need a $800 per month payment, I need to find another way to do it.
That's it for today! In a future article, we'll explore other ways that we might be able to decrease our monthly payment.
