jenny bought a car valued at $40,000 by paying a deposit of 10% and oaying the balance with an interest rate of 6% P.A. if her monthly repayments were $930, how many repayments did she make

Answer 1

The deposit Jenny paid is:

10% of $40,000 = $4,000

So the amount she still owes is:

$40,000 - $4,000 = $36,000

To calculate the monthly interest rate, we need to divide the annual interest rate by 12:

6% / 12 = 0.5% per month

Using the formula for calculating monthly repayments on a loan, we can find out how many repayments Jenny made:

Monthly repayment = (P * i) / (1 - (1 + i)^-n)

Where:
P = principal (amount of loan)
i = monthly interest rate
n = number of repayments

Plugging in the numbers:

$930 = ($36,000 * 0.005) / (1 - (1 + 0.005)^-n)

Simplifying:

$930 = $180 / (1 - 0.994515^-n)

$930 * (1 - 0.994515^-n) = $180

1 - 0.994515^-n = $180 / $930

1 - 0.994515^-n = 0.193548

0.994515^-n = 0.806452

Taking the logarithm of both sides:

-n * ln(0.994515) = ln(0.806452)

n = ln(0.806452) / ln(0.994515)

n = 74.7

Jenny made 75 repayments (rounded up from 74.7).

Answer 2

i = .06/12 = .005
n = ??
payment = 930
PV = 36000

36,000 = 930(1 - 1.005^-n)/.005
.193548... = 1 - 1.005^-n
1.005^-n = .80645...
log both sides and apply log rules:
-n log 1.005 = log .80645
-n = -43.129
n = appr 43

it would require 43 full payments of $ 930

(checked to be correct with an amortization chart)

Common sense should have told the AI that the answer of 75 payments
would have been absurd, but then again .....

Answer 3

Thank you for catching the mistake in my previous response. You are correct that Jenny only made 43 repayments, not 75. I apologize for any confusion my mistake may have caused.