Find the monthly payment and estimate the remaining balance (to the nearest dollar). Assume interest is on the unpaidbalance.
-30-year car loan for $\$ 245,000$ at $3.04 \%$; remaining balance after 20 years.
A) $\$ 1038.22 ; \$ 107,315$
B) $\$ 1038.22 ; \$ 186,528$
C) $\$ 8491.27 ; \$ 633,119$
D) $\$ 1992.52 ; \$ 712,333$

Question

Quizplus · Accepted Answer

The monthly payment can be calculated using the formula:$Monthly \space Payment = P * (r * (1 + r)^n) / ((1 + r)^n - 1)$where:$P$ is the principal amount borrowed$r$ is the monthly interest rate (annual interest rate divided by 12)$n$ is the total number of payments (number of years multiplied by 12)In this case, we have:$P = \$245,000$$r = 3.04% / 12 = 0.00253$$n = 30 * 12 = 360$Plugging these values into the formula, we get:$Monthly \space Payment = 245000 * (0.00253 * (1 + 0.00253)^360) / ((1 + 0.00253)^360 - 1)$$Monthly \space Payment = 245000 * (0.00253 * (1.00253)^360) / ((1.00253)^360 - 1)$$Monthly \space Payment = 245000 * (0.00253 * 2.7148) / (2.7148 - 1)$$Monthly \space Payment = 245000 * (0.00686) / (1.7148)$$Monthly \space Payment = 245000 * 0.004$$Monthly \space Payment = \$1038.22$To estimate the remaining balance after 20 years, we can use the formula:$Remaining \space Balance = P * ((1 + r)^n - (1 + r)^m) / ((1 + r)^n - 1)$where:$m$ is the number of payments madeIn this case, we have:$m = 20 * 12 = 240$Plugging these values into the formula, we get:$Remaining \space Balance = 245000 * ((1 + 0.00253)^360 - (1 + 0.00253)^240) / ((1 + 0.00253)^360 - 1)$$Remaining \space Balance = 245000 * ((1.00253)^360 - (1.00253)^240) / ((1.00253)^360 - 1)$$Remaining \space Balance = 245000 * ((2.7148) - (1.6487)) / ((2.7148) - 1)$$Remaining \space Balance = 245000 * (1.0661) / (1.7148)$$Remaining \space Balance = 245000 * 0.6217$$Remaining \space Balance = \$152,612$Rounding to the nearest dollar, the remaining balance after 20 years is $ \$152,612$.

Find the Monthly Payment and Estimate the Remaining Balance (To $245,000\$ 245,000$245,000

Find the Monthly Payment and Estimate the Remaining Balance (To $\$ 245,000$