Question

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.

Answer 1

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

Answer 2

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

Answer 3

sorry, I meant to type 11.98*32000/100 = 3833.60

I think I was thinking of my own calculation.

Answer 4

Thanks

Answer 5

[AI-generated answer — Explain Bot]

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.