In order to make some home improvements, a home owner spent $40,000. He paid 20% as a down payment and financed the balance of the purchase with a 36-month fixed installment loan with an APR of 7.5%. Determine the home owner’s a) total finance charge and b) monthly payment..
Use this partial APR table for finance charge per $100
Payments
Number Annual percentage rate
ofPmts 7.00% 7.50% 8.00% 8.50%
24 7.45 8.00 8.54 9.09
30 9.30 9.98 10.66 11.35
36 11.16 11.98 12.81 13.64
Each entry in the table represents finance charge/$100 at the given terms.
the monthly rate i is .075/12 = .00625
He finances 32,000 dollars, so
32000 = paym[1 - 1.00625^(-36)]/.00625
this gave me a payment of $995.40
his total interest charge is 32000 - 36*995.40
= $3834.36
If I use your chart, the interest charge would be 11.96*36 = $3833.60 a difference of 76 cents.
I was using the accepted compound interest formula
Present value = paym(1 - (1+i)^-n)/i
the interest charge would be 11.96*36 = $3833.60 a difference of 76 cents
Hi how did you get the 3833.6 from multiplying 11.96*36.
Thanks
sorry, I meant to type 11.98*32000/100 = 3833.60
I think I was thinking of my own calculation.
Thanks
To determine the homeowner's total finance charge, we need to calculate the finance charge on the financed balance. Here's how you can do it:
1. Calculate the down payment amount: Since the homeowner paid 20% as a down payment, multiply the total amount spent ($40,000) by 20% (or 0.20) to find the down payment amount.
Down Payment = $40,000 * 0.20 = $8,000
2. Calculate the financed balance: Subtract the down payment amount from the total amount spent to get the financed balance.
Financed Balance = $40,000 - $8,000 = $32,000
3. Determine the finance charge per $100: Use the provided partial APR table to find the finance charge per $100 for a 36-month loan term with an APR of 7.5%.
From the table, we can see that the finance charge per $100 for a 36-month loan term with an APR of 7.5% is 11.98.
4. Calculate the finance charge on the financed balance: Divide the financed balance by $100, then multiply the result by the finance charge per $100 to find the finance charge on the financed balance.
Finance Charge = ($32,000 / $100) * 11.98 = $3,833.60
Therefore, the homeowner's total finance charge is $3,833.60.
To determine the monthly payment, we can use the formula for calculating monthly payments on a fixed installment loan:
Monthly Payment = (Financed Balance + Finance Charge) / Number of Payments
1. Calculate the monthly payment:
Monthly Payment = ($32,000 + $3,833.60) / 36
Monthly Payment = $35,833.60 / 36
Monthly Payment = $995.37 (rounded to the nearest cent)
Therefore, the homeowner's monthly payment will be approximately $995.37.