# Loan with floating interest [closed]

I have taken a 7 years loan of 450 000 for a car in January 2017 with monthly payment of 7077. The interest rate was 8.25% which means that the total repayment is 593878 after 7 years. As from November 2017 till now, since the interest rate has changed, I have been paying 6972.69 par month. Can any one please tell me what is the new interest rate since November 2017 and also how much I left I need to repay. I am at lost about how to calculate that with floating interest.

• what currency is that? and is this a homework question? – Fattie Jul 15 '18 at 13:41
• Are you sure the initial payment isn't 7070? – Chris Degnen Jul 15 '18 at 13:57
• Calculating payments from total: `593878/7/12 = 7069.98` – Chris Degnen Jul 15 '18 at 15:15

Similar to the answer to this question:-

Calculate mortgage rate with a different interest rate after certain years

``````s = principal
r = monthly interest rate
n = number of months
d = monthly payment

s = 450000
r = 8.25/100/12
n = 7*12
``````

Payment amount to pay off at 8.25% over 7 years (ref. formula)

``````d = r (1 + 1/((1 + r)^n - 1)) s = 7069.98
``````

However, the interest rate changes after 10 months.

For calculations with rate changes calculate the principal remaining at the time the rate changes, then treat the next period as a fresh amortisation.

Calculating the principal remaining after 10 months, `x`, resetting the value of `s`

``````x = 10
s = (d + (1 + r)^x (r s - d))/r = 408984.76
``````

Continuing with new figures.

``````n = 7*12 - x
d = 6972.69
``````

Numerically solving annuity equation `s = (d - d (1 + r)^-n)/r` for `r`

``````r = 0.00647044
``````

The new interest rate is `12 r = 7.76452 %`