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You can afford a $250 per month car payment. You've found a 3 year loan at 5% interest. How big of a loan can you afford? Enter an integer or decimal number [more.].] Add Work Check Answer

You can afford a $250 \$ 250 per month car payment. You've found a 33 year loan at 5% 5 \% interest. How big of a loan can you afford?\newline$\$\\\newlineEnter an integer or decimal number [more.].

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Q. You can afford a $250 \$ 250 per month car payment. You've found a 33 year loan at 5% 5 \% interest. How big of a loan can you afford?\newline$\$\\\newlineEnter an integer or decimal number [more.].
  1. Calculate Monthly Interest Rate: To solve this problem, we need to use the formula for an installment loan payment, which is typically represented as P=rPV1−(1+r)−nP = \frac{rPV}{1 - (1 + r)^{-n}}, where PP is the monthly payment, rr is the monthly interest rate, VV is the loan amount (which we are trying to find), and nn is the total number of payments.\newlineFirst, we need to convert the annual interest rate to a monthly interest rate by dividing by 1212 (since there are 1212 months in a year).\newlineAnnual interest rate: 5%5\%\newlineMonthly interest rate: 5%12\frac{5\%}{12}
  2. Determine Total Number of Payments: Now, let's calculate the monthly interest rate in decimal form.\newlineMonthly interest rate (decimal): 5100÷12=0.00416666667\frac{5}{100} \div 12 = 0.00416666667\newlineNext, we need to determine the total number of payments over the 33 years.\newlineTotal number of payments (nn): 3 years×12 months/year=36 months3 \text{ years} \times 12 \text{ months/year} = 36 \text{ months}
  3. Plug Values into Formula: We can now plug the values into the formula to solve for VV, the loan amount.P=$250P = \$250 per monthr=0.00416666667r = 0.00416666667 per monthn=36n = 36 monthsUsing the formula: $250=(0.00416666667×V)1−(1+0.00416666667)−36\$250 = \frac{(0.00416666667 \times V)}{1 - (1 + 0.00416666667)^{-36}}
  4. Isolate V: To isolate V, we need to multiply both sides of the equation by the denominator on the right side and then divide by the monthly interest rate.\newline$250×(1−(1+0.00416666667)−36)=0.00416666667×V\$250 \times (1 - (1 + 0.00416666667)^{-36}) = 0.00416666667 \times V
  5. Calculate Value of (1−(1+0.00416666667)−36)(1 - (1 + 0.00416666667)^{-36}): Now we need to calculate the value of (1−(1+0.00416666667)−36)(1 - (1 + 0.00416666667)^{-36}).(1+0.00416666667)−36=1(1+0.00416666667)36(1 + 0.00416666667)^{-36} = \frac{1}{(1 + 0.00416666667)^{36}} We calculate (1+0.00416666667)36(1 + 0.00416666667)^{36} using a calculator.(1+0.00416666667)36≈1.157625687(1 + 0.00416666667)^{36} \approx 1.157625687 Now, we take the reciprocal of this value.11.157625687≈0.8639053255\frac{1}{1.157625687} \approx 0.8639053255 Then, we subtract this value from 11.1−0.8639053255≈0.13609467451 - 0.8639053255 \approx 0.1360946745
  6. Solve for V: We now have all the values needed to solve for V.\newline$250×0.1360946745=0.00416666667×V\$250 \times 0.1360946745 = 0.00416666667 \times V\newline$34.023668625=0.00416666667×V\$34.023668625 = 0.00416666667 \times V\newlineTo find V, we divide both sides by the monthly interest rate.\newlineV=$34.0236686250.00416666667V = \frac{\$34.023668625}{0.00416666667}\newlineV≈$8164.80V \approx \$8164.80

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