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Virgin Credit Card Balance Transfer

Hi,

I have a Virgin Credit Card offer of 3.5% money transfer with 0% fee until October 27. Have £16435 available to transfer to my bank and then invest at 4.5% fixed for 1 year with invested and thereafter rate to be confirmed. 

I've run some figures through AI and it's come up with the following, do you think it's worth borrowing this amount until October 27 for the return AI is saying below, assuming 4.5% savings for the duration? I just dont seem to be getting offered anything better and haven't for about 12 months or so.

✅ 1. Loan Repayment Structure
Initial loan balance
𝐿
0
=
16
,
435
+
575.23
=
£
17
,
010.23
L
0
 ​

=16,435+575.23=£17,010.23
Monthly payment
Payment
𝑡
=
0.02
×
𝐿
𝑡
Payment
t
 ​

=0.02×L
t
 ​


Balance shrinks geometrically:

𝐿
𝑛
=
𝐿
0
×
0.98
𝑛
L
n
 ​

=L
0
 ​

×0.98
n

For 22 months:

0.98
22
0.641
0.98
22
≈0.641
𝐿
22
=
17
,
010.23
×
0.641
£
10
,
918
L
22
 ​

=17,010.23×0.641≈£10,918
Total payments made over 22 months
Total paid
=
𝐿
0
𝐿
22
=
17
,
010.23
10
,
918
£
6
,
092
Total paid=L
0
 ​

−L
22
 ​

=17,010.23−10,918≈£6,092
✅ 2. Investment Growth at 4.5% APR

Investment amount:

16
,
435
16,435

Growth factor for 22 months:

(
1
+
0.045
)
22
/
12
1.083
(1+0.045)
22/12
≈1.083

Investment value:

𝐹
𝑉
=
16
,
435
×
1.083
£
17
,
793
FV=16,435×1.083≈£17,793
🧮 Final cash position

You must pay off the remaining loan balance after month 22:

Remaining balance
=
£
10
,
918
Remaining balance=£10,918

So after making all payments and clearing the balance:

Profit
=
𝐹
𝑉
Total Paid
Remaining Balance
Profit=FV−Total Paid−Remaining Balance
Profit
=
17
,
793
6
,
092
10
,
918
Profit=17,793−6,092−10,918
Profit
£
783
Profit≈£783
⭐ You would make approximately £780 profit at 4.5% APR.
✅ 3. Break-Even APR (profit = 0)

You break even when:

𝐹
𝑉
=
𝐿
0
FV=L
0
 ​


i.e.

16
,
435
×
(
1
+
𝑟
)
22
/
12
=
17
,
010.23
16,435×(1+r)
22/12
=17,010.23
(
1
+
𝑟
)
22
/
12
=
17
,
010.23
16
,
435
=
1.035
(1+r)
22/12
=
16,435
17,010.23
 ​

=1.035

Raise both sides to 12/22:

1
+
𝑟
=
1.035
12
/
22
1+r=1.035
12/22

Compute exponent:

12
/
22
=
0.545
12/22=0.545

1.035
0.545
1.0190
1.035
0.545
≈1.0190

So:

𝑟
0.019
=
1.9
%
 APR
r≈0.019=
1.9% APR
 ​

🎯 Final Summary
Item Result
Profit at 4.5% APR ~£780
Break-even APR ≈ 1.9%

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