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A More Involved Balance Transfer Offer
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THE SCENARIO
Last time, I talked about a balance transfer offer I got in the mail, and I simplified the problem using an assumption. This time, I'll change the assumption to more closely model reality.
To review, the card has a $7,000 credit limit and 0% interest on balance transfers over the first 21 months after the transfer. The fee to do the transfer is 5% of the transferred amount, which is added to the balance on the new card.
Whereas last time, we assumed that no payments were due during the 21 months, this time we'll assume that 2% of the original balance is owed each month.
The question: If I were to get this card and transfer a $6,500 balance to it, what would my effective annual interest rate be if I pay it off at the end of the 21 months, assuming that I pay 2% of the original balance each month?
THE SOLUTION
This one is pretty straightforward, and has a few parts.
- Find the initial balance
- Find the monthly payment
- Find the final balance due
- Find the effective interest rate
First things first, make sure the calculator is using 12 Payments per Year.
Step 1: Initial Balance
If we transfer $6,500 to the card and there's a 5% fee, we'll start out owing $6,500 x 5% = $325 more than we transferred.
$6,500 + $325 =
$6,825. This is our initial balance.
Step 2: Monthly Payment
The monthly payment is 2% of the initial balance. 2% of $6,825 is $6,825 x 2% =
$136.50.
Step 3: Ending Balance
N: 21 (The offer is for 21 months interest-free)
I/YR: 0 (The card charges 0% interest during this period)
PV: 6,825 (I'm transferring a $6,500 balance to the card, but I start out owing 5% more)
PMT: -136.50 (The monthly payment is $136.50)
FV: (This is what I'm trying to find)
After the 21 months, I'll still owe the company $3,958.50.
Step 4: Effective Rate
First things first, make sure the calculator is using 12 Payments per Year.
N: 21 (The offer is for 21 months interest-free)
I/YR: (This is what I'm trying to find)
PV: 6,500 (I'm transferring a $6,500 balance to the card, which means that I'm borrowing $6,500 from the card company)
PMT: -136.50 (The monthly payment is $136.50)
FV: -3,958.50 (I'll have to pay back $3,958.50 at the end)
The effective interest rate on the '0% interest' 21-month loan from the credit card company is 3.50%. Not zero, but much lower than whatever card I'd be transferring the balance from.
To review,
last time we determined that the effective rate was 2.79%, but this time the rate is higher. The reason for this is that the longer we wait before paying the money back, the lower the effective rate will be. Since
last time, we didn't pay a penny until the end of the 21 months, but this time we started paying off the balance right away, the effective rate this time is somewhat higher than last time.
What do you think? Would you prefer to pay down the balance slowly over the 21 months, or wait until the end to pay off the whole thing? Why do you feel this way? Let us know in the comments!
