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Reader Question: Should I Pay Off My Car Loan Early?
By JLP | November 11, 2007
Here’s a recent email (edited slightly) I received from a reader regarding whether or not to pay off a car early:
Hello,
I am wondering if you can help me out with some investment math. I can’t tell if i’m doing something wrong, but I’m too close to the data to see it. here’s the question -
I have a car loan that goes through 3/2011 and the current balance is $18,000. My monthly payment is $490 and the interest rate is 6.25%. I have enough cash to pay the loan off, but I can’t figure out if it the right thing to do.
Here’s what I figured:
Keeping the loan:
41 months remaining on loan
$18k loan balance
$490 payment
$20,090 total paid in loan + interest ($490 41) $2,090 in interest paid$18k in savings account
4% interest rate (currently it’s at 4.50, but i’m lowering for possible future drops)
41 months
$20,986 balance at end of 41st month
$2,986 in interest earned+$970 if I keep the loan
Pay the loan off:
$490 monthly payment to savings
4% interest
41 months
$21,754 at end of 41st month
$1,664 interest earned$1,664 - $970 = $694 more money earned if I pay the loan off now.
I also have pros/cons
Paying early pros: no debt, more money earned at end of original loan date.
Payoff early cons: depleted cash reserves, takes 35 months to reach original cash balance, must save that 490 to savings every month.
Keep loan pros: forces me to “save” or keeps me from recklessly spending extra cash, keep Cash reserves.
Keep loan cons: costs $200 a year in interest ($694/3.45 years), credit score impact.
I guess the real question is, can I live without having the cash over the next 3 years or put another way, am I willing to pay $200 a year to keep $18k.
Any help you provide is greatly appreciated. I didn’t use exact numbers but they are close enough. Thanks.
Thomas
Here’s my response:
Although I get different numbers when I perform the math, the end result is the same.
Keeping the Loan
First off, I’ll show you how I did the math:
If Thomas keeps the loan and invests the $18,000 at 4% per year, at the end of 41 months, he will have a cash balance of $20,631.
Remember the formula for future value is:
FV = PV × (1 + i)n
where:
i = .04 ÷ 12 = 0.003333 (remember we are using monthly numbers so we have to adjust the annual interest rate to a monthly rate)
n = number of months
Plugging in our numbers, we get a formula that looks like this:
FV = $18,000 × (1 + .003333)41
FV = $18,000 × 1.1462
FV = $20,631
Paying Off the Loan
If Thomas pays off the loan early, he will lose out on the growth of the $18,000 over the 41 month period but he will be able to save his $490 per month at 4%. Going this route, at the end of 41 months, he will have a cash balance of $21,561.
To figure this out, we’ll have to use the future value of an annuity formula, which looks like this:
FVIFA = [((1 + i)n - 1) ÷ i] × (1 + i)
Plugging in our numbers, we get a formula that looks like this:
FVIFA = [(1.14618541 - 1) ÷ .003333] × 1.003333
FVIFA = [.14618541 ÷ .003333] × 1.003333
FVIFA = 43.85562292 × 1.003333
FVIFA = 44.00180833
Now we simply multiply the monthly savings amount ($490) by the FVIFA solved for above and we get an ending cash balance of $21,561.
The Bottom Line
Based on these numbers, Thomas comes out ahead $930 ($21,561 - $20,631 = $930) by using his $18,000 in savings to pay off his car and then investing the monthly payment ($490) at 4%. This really shouldn’t be a surprise to anyone since his loan is costing him more than he can earn in a savings account. Yes, theoretically he could invest the $18,000 in stocks for potentially bigger returns but I didn’t mention this because that’s not what he asked for. Therefore I assumed he wanted to keep his $18,000 liquid if he decided not to pay off his car early.
Those are my thoughts. Did I miss anything?
Good luck Thomas!
Topics: Budgeting, Financial Math Basics, Miscellaneous |
