Andres Michael bought a new boat. He took out a loan for $23,980 at 3.75% interest for 4 years. He made a $4,470 partial payment at 4 months and another partial payment of $3,180 at 9 months. How much is due at maturity?
To find the amount due at maturity, we need to calculate the remaining balance after the partial payments and the accumulated interest.
Step 1: Calculate the interest per month.
Interest Rate = 3.75% = 0.0375
Monthly Interest Rate = 0.0375 / 12 = 0.003125
Step 2: Calculate the remaining balance after the 4-month partial payment.
Principal = $23,980
Partial Payment = $4,470
Remaining Balance = Principal - Partial Payment
Remaining Balance = $23,980 - $4,470 = $19,510
Step 3: Calculate the interest accumulated for the remaining time.
Time remaining for 4 years = 4 years - 4 months = 3 years and 8 months
Months remaining = 3 years * 12 months + 8 months = 44 months
Interest Accumulated = Remaining Balance * Monthly Interest Rate * Months Remaining
Interest Accumulated = $19,510 * 0.003125 * 44 = $2,700.25
Step 4: Calculate the remaining balance after the 9-month partial payment.
Partial Payment = $3,180
Remaining Balance = Remaining Balance - Partial Payment - Interest Accumulated
Remaining Balance = $19,510 - $3,180 - $2,700.25 = $13,629.75
Step 5: Calculate the final amount due at maturity.
Amount Due at Maturity = Remaining Balance + Interest Accumulated
Amount Due at Maturity = $13,629.75 + $2,700.25 = $16,330
Therefore, the amount due at maturity is $16,330.
To calculate the amount due at maturity, we need to consider the loan amount, interest rate, loan duration, and the partial payments made.
First, let's calculate the interest accrued on the loan for the full loan duration of 4 years (48 months). To do this, we'll use the formula:
Interest = Principal * Rate * Time
Interest = $23,980 * 0.0375 * 4
Next, we need to calculate the remaining principal amount after the two partial payments. To do this, we subtract each partial payment from the original loan amount.
Remaining Principal = Loan Amount - Partial Payment 1 - Partial Payment 2
Remaining Principal = $23,980 - $4,470 - $3,180
Finally, we add the interest accrued to the remaining principal to find the amount due at maturity.
Amount Due at Maturity = Remaining Principal + Interest
Now let's calculate the values:
Interest = $23,980 * 0.0375 * 4 = $3,594
Remaining Principal = $23,980 - $4,470 - $3,180 = $16,330
Amount Due at Maturity = $16,330 + $3,594 = $19,924
Therefore, the amount due at maturity would be $19,924.