Matthew purchased a washer and dryer for $1,965 using an 18-month deferred payment plan with an interest rate of 18.43%. What is the balance after the deferment period if payments of $65 were made each month?

$1,965.00

$2,585.30

$795.00

$1,415.30

Question

Matthew purchased a washer and dryer for $1,965 using an 18-month deferred payment plan with an interest rate of 18.43%. What is the balance after the deferment period if payments of $65 were made each month?

 $1,965.00

 $2,585.30

 $795.00

 $1,415.30

amistre64 · Answer

this is just a balance equation ...

amistre64 · Answer

1965k^(18) - 65(1-k^(18))/(1-k)

amistre64 · Answer

instead of having to pay a set minimum payment to zero out the loan in a certain time span; they just created their own payment structure

dumbcow · Answer

@amistre64 , it doesn't match any of the answers though
i worked it out twice and got 1249

amistre64 · Answer

i get 1249 as well

dumbcow · Answer

does deferred mean no interest is applied for those 18 months
the 65 is just simply deducted from balance?

amistre64 · Answer

not unless it says no interest accruing; it means that there is no payments necessary during the period

dumbcow · Answer

yeah and thats never the case...never do deferred loans haha

amistre64 · Answer

Bo = Bo

B1 = Bo(k) - P

B2 = (Bo(k) - P)k - P = Bok^2 -Pk -P

B3 = Bok^3 -Pk^2 -Pk -P

Bn = Bok^n -Pk^(n-1) -Pk^2 -Pk -P

$$B_n=B_ok^n-P\frac{1-k^n}{1-k}$$
allowing for k to clean up that compounding mess

amistre64 · Answer

since n is measured in months;  n = 18 in this case

dumbcow · Answer

based on the choices it must be option D
none of others make sense...balance would change and be less than if no payments were made but greater than option where no interest accrues

amistre64 · Answer

i agree

amistre64 · Answer

then that would be a defered period of about 14 to 15 months :)