Andres Michael bought a new boat. He took out a loan for $24,010 at 4.5% interest for 4 years. He made a $4,990 partial payment at 4 months and another partial payment of $2,660 at 9 months. How much is due at maturity?
Well, it seems that Andres Michael is really trying to "sail" through this boat loan. Let's calculate the amount that is due at maturity, shall we?
First, let's calculate the remaining principal after the partial payments. At 4 months, Andres made a payment of $4,990, so the principal becomes $24,010 - $4,990 = $19,020.
Next, at 9 months, he made another payment of $2,660, so the principal further decreases to $19,020 - $2,660 = $16,360.
Now, let's calculate the interest for the remaining 3 years (36 months) at a rate of 4.5%. The total interest is ($16,360 * 4.5% * 3) / 12 = $1,476.60.
Adding the remaining principal and the interest, we get $16,360 + $1,476.60 = $17,836.60.
So, at maturity, Andres Michael will still owe $17,836.60. Let's hope he doesn't "wave" goodbye to his money!
To calculate the amount due at maturity, we need to consider the initial loan amount, the interest rate, and the partial payments made.
1. Calculate the interest accrued on the loan:
Principal = $24,010
Interest rate = 4.5%
Time (in years) = 4
Interest = Principal * Interest rate * Time
= $24,010 * 0.045 * 4
= $4,322.20
2. Deduct the partial payments made:
Partial payment 1 = $4,990
Partial payment 2 = $2,660
Total partial payments = $4,990 + $2,660
= $7,650
3. Subtract the total partial payments from the initial loan amount:
Amount due at maturity = Principal + Interest - Total partial payments
= $24,010 + $4,322.20 - $7,650
= $20,682.20
Therefore, the amount due at maturity is $20,682.20.
To find out how much is due at maturity, we need to calculate the remaining balance after the partial payments.
Step 1: Calculate the annual interest rate
Since the loan has an interest rate of 4.5%, we need to determine the monthly interest rate by dividing it by 12 (number of months in a year).
Monthly interest rate = 4.5% / 12 = 0.045 / 12 = 0.00375
Step 2: Calculate the number of months remaining
Since the loan term is for 4 years (48 months), and payments were made at 4 months and 9 months, we need to calculate the remaining months.
Remaining months = Total months - Months when payment was made
Remaining months = 48 - (4 + 9) = 48 - 13 = 35
Step 3: Calculate the remaining balance after the partial payments
For the first partial payment:
Interest on first partial payment = Monthly interest rate * Remaining balance before payment
Interest on first partial payment = 0.00375 * $24,010 = $90.03
Remaining balance after first partial payment = Remaining balance before payment - Partial payment amount + Interest on first partial payment
Remaining balance after first partial payment = $24,010 - $4,990 + $90.03 = $19,110.03
For the second partial payment:
Interest on second partial payment = Monthly interest rate * Remaining balance before payment
Interest on second partial payment = 0.00375 * $19,110.03 = $71.79
Remaining balance after second partial payment = Remaining balance before payment - Partial payment amount + Interest on second partial payment
Remaining balance after second partial payment = $19,110.03 - $2,660 + $71.79 = $16,521.82
Step 4: Calculate the due amount at maturity (remaining balance after all partial payments)
The due amount at maturity is the remaining balance after all partial payments have been deducted.
Due amount at maturity = Remaining balance after second partial payment
Due amount at maturity = $16,521.82
Therefore, the amount due at maturity is $16,521.82.
Assuming simple interest (not stated otherwise)
after 2 months, the interest is $24500*(1/6)*,045=$183.75
the new principal is $24683.75 minus the $4500 payment to yield $20183.75
the interest the next four months is 1/3 year, so the total is $302.76 for principal now of $20486.51
subtract 3000 and have $17486.51 for 18 months, or 1.5 years
That is $1180.34 interest, calculated the same way as the other two.
The amount due is $18666.85