Scott purchases a piano costing $2,630 by taking out a 13% add-on interest installment loan. The loan requires a 15% down payment and equal monthly payments for 5 years. How much are Scott's monthly payments?
Surely for a time frame of 5 years, simple interest would not be used.
so i = .13/12 = .0108333...
amount financed = 2630(.85) = 2235.50
amount of loan ---- x
x(1 - 1.0108333..^-60)/.0108333..) = 2235.5
I get
x = $ 50.86
Apparently it used to be done this way, yielding a payment which is much too high.
interest on the "total" amount = 2235.5(.13)(5) = 1453.08
amount owing (as if you made no payments) = 1453.08 + 2235.5 = 3688.58
monthly payment = 3688.58/60 = 61.47
I even found a video showing this method:
https://www.youtube.com/watch?v=NwJ52OkkmXM
To find Scott's monthly payments, we need to first calculate the amount he borrowed and then determine the monthly payments based on the duration of the loan.
1. Calculate the amount borrowed:
The loan requires a 15% down payment on the piano, which means Scott paid 15% of $2,630 as a down payment.
Down payment = 15% of $2,630 = 0.15 * $2,630 = $394.50
The remaining amount he borrowed is the purchase price minus the down payment.
Amount borrowed = $2,630 - $394.50 = $2,235.50
2. Calculate the total interest paid over the loan period:
The loan is an add-on interest installment loan with 13% add-on interest. This means the interest is calculated based on the original amount borrowed, not the remaining balance.
Total interest paid = 13% of $2,235.50 = 0.13 * $2,235.50 = $290.07
3. Determine the total amount to be paid back:
Total amount to be paid back = Amount borrowed + Total interest paid
Total amount to be paid back = $2,235.50 + $290.07 = $2,525.57
4. Calculate the number of monthly payments:
The loan duration is 5 years, so there are 5 * 12 = 60 monthly payments.
5. Calculate the monthly payment amount:
Monthly payment = Total amount to be paid back / Number of monthly payments
Monthly payment = $2,525.57 / 60 = $42.09
Therefore, Scott's monthly payments for the piano would be approximately $42.09.