Financial calculation question: variable interest rate

[Dave Britten]

Suppose I open a home equity line of credit that has a 1.99% introductory rate for 6 months. Then I immediately finance something for, say $4000. After 6 months, the interest rate increases to 2.99%. How would I go about calculating 12 equal payments to have the financed amount fully paid off at the end of 12 months?

Note I'm assuming such a credit line has beginning-period payments like a credit card, and the interest will compound at 1.99% APR six times before changing to 2.99%.

[fhub]

(07-04-2015 09:55 PM)Dave Britten Wrote:  Suppose I open a home equity line of credit that has a 1.99% introductory rate for 6 months. Then I immediately finance something for, say $4000. After 6 months, the interest rate increases to 2.99%. How would I go about calculating 12 equal payments to have the financed amount fully paid off at the end of 12 months?

Note I'm assuming such a credit line has beginning-period payments like a credit card, and the interest will compound at 1.99% APR six times before changing to 2.99%.

Well, the TVM equation for this problem is:
(it's easy to calculate PMT=... from it)

PV*(1+i1)^6*(1+i2)^6 + PMT*((1+i1)^6-1)/i1*(1+i1)*(1+i2)^6 + PMT*((1+i2)^6-1)/i2*(1+i2)=0

PV=4000, i1 and i2 are the monthly interest rates of 1.99% and 2.99% (depending on whether APR means nominal or effective annual rate), i.e. either i1=1.99%/12 (for nom. APR) or i1=(1+1.99%)^(1/12)-1 (for eff. APR).

PS: the result is PMT=-$336.728 (for nom. APR) and PMT=-$336.689 (for eff. APR).

Franz

[Dave Britten]

(07-05-2015 10:16 AM)fhub Wrote:  

(07-04-2015 09:55 PM)Dave Britten Wrote:  Suppose I open a home equity line of credit that has a 1.99% introductory rate for 6 months. Then I immediately finance something for, say $4000. After 6 months, the interest rate increases to 2.99%. How would I go about calculating 12 equal payments to have the financed amount fully paid off at the end of 12 months?

Note I'm assuming such a credit line has beginning-period payments like a credit card, and the interest will compound at 1.99% APR six times before changing to 2.99%.

Well, the TVM equation for this problem is:
(it's easy to calculate PMT=... from it)

PV*(1+i1)^6*(1+i2)^6 + PMT*((1+i1)^6-1)/i1*(1+i1)*(1+i2)^6 + PMT*((1+i2)^6-1)/i2*(1+i2)=0

PV=4000, i1 and i2 are the monthly interest rates of 1.99% and 2.99% (depending on whether APR means nominal or effective annual rate), i.e. either i1=1.99%/12 (for nom. APR) or i1=(1+1.99%)^(1/12)-1 (for eff. APR).

PS: the result is PMT=-$336.728 (for nom. APR) and PMT=-$336.689 (for eff. APR).

Franz

Excellent, thanks. Now, if I wanted to generalize this a bit before entering it into my 17BII, would this be the correct way to have optional begin/end-period payments, and tack on FV (in case it needs to be non-zero)? (B = 1 for beginning, 0 for ending)

PV*(1+i1)^n1*(1+i2)^n2 + PMT*((1+i1)^n1-1)/i1*(1+B*i1)*(1+i2)^n2 + PMT*((1+i2)^n2-1)/i2*(1+B*i2) + FV = 0

EDIT: That seems to be working, based on the results I'm getting and then comparing to the built-in TVM solver (doing it piecewise, i.e. solve for FV with n=6, change the sign and stuff it back in PV, update the interest rate, and solve for FV again). Error is a good 8 decimal places out, and it's possible that's just because I'm running the solver in Fix 8 mode.

Corrections still welcome if anybody finds any problems with it.

[fhub]

(07-06-2015 02:37 PM)Dave Britten Wrote:  Corrections still welcome if anybody finds any problems with it.

No corrections necessary, your general formula is perfect!

BTW, is this (changing the insterest rate during the payment periods) a usual situation in your country?

Franz

[Dave Britten]

(07-07-2015 08:36 AM)fhub Wrote:  

(07-06-2015 02:37 PM)Dave Britten Wrote:  Corrections still welcome if anybody finds any problems with it.

No corrections necessary, your general formula is perfect!

BTW, is this (changing the insterest rate during the payment periods) a usual situation in your country?

Franz

I don't think it's terribly common. Probably just for credit cards, credit lines, and other revolving balance sort of accounts. I was offered a home equity credit line with a promotional introductory rate of 1.99% for 6 months, after which it would go to its normal rate of around 2.74-2.99%. I wanted to play with a few numbers to get an idea of finance charges over 6 months, 12 months, etc. but didn't know how to calculate a uniform payment for that situation. Thanks for your help!