Calculating the balance and cash price on a loan plan.

[saneye93]

Are my answer correct for part (a)?
I need assistance with part (b) please, where the question marks are.

Terms for a loan plan are: i) 20% downpayment, ii) 10% added to the balance to make the total balance, iii) total balance paid in 12 equal monthly payment.

(a) Cash price of a suite is $2475. Using loan plan:
i) Downpayment - 495
ii) Balance + Interest - 2178
iii) Monthly - 181.50

(b) Another person buys a suite using the loan purchase and pays $154 per month. Calculate:
i) total balance - $1848
ii) balance before interest - $1663.20 (not sure if this correct)
iii) cash price (no clue what to do with the 20%)
iv) total amount paid under the hire purchase plan

 

[HallsofIvy]

Are my answer correct for part (a)?
I need assistance with part (b) please, where the question marks are.

Terms for a loan plan are: i) 20% downpayment, ii) 10% added to the balance to make the total balance, iii) total balance paid in 12 equal monthly payment.

(a) Cash price of a suite is $2475. Using loan plan:
i) Downpayment - 495

Yes, the downpayment is 0.20($2475)= $495. I might fault you for not including the "$".

ii) Balance + Interest - 2178

.
The balance is $2475- 495= $1980. 10% of that is $198 so $1980+ 198= $2178.
Yes, you are correct.

iii) Monthly - 181.50

And $2178/12= $181.5

Well done!

(b) Another person buys a suite using the loan purchase and pays $154 per month. Calculate:
i) total balance - $1848

Assuming "total balance" is "balance + interest" as before, 12($154)= $1848. Yes, that is correct.

ii) balance before interest - $1663.20 (not sure if this correct)

For the last two you need ALGEBRA!
Let the balance be "x". Then 10% of the balance is 0.10x so balance plus interest is x+ 0.10x= =1.10x= $1848. x= $1848/1.1= $1680, not "$1663.20".

iii) cash price (no clue what to do with the 20%)

Let the original cash price be P. The 20% downpayment is .20P. After that downpayment, the balance is P- 0.20P= 0.80P= $1680. P= $1680/.8= $2400.

iv) total amount paid under the hire purchase plan

The $2400 downpayment plus 12($154)= $2400+ $1848= $4248.

 

[saneye93]

Thank you! Just two questions:
i) Should the cash price be $1680/0.8=$2100 instead of $2400?
ii) For the total amount why did you add $2400 if the loan plan only asks for 20% of the cash price? I see you stated $2400 as the downpayment, is it not the cash price?

 

[HallsofIvy]

Yes, the $2400 was an error on my part, it should be $2100 down payment.

For (ii) surely you understand that a "downpayment" is NOT the total price? The "cash price" is the total amount you have to pay, not including interest.