Sasha took in a car loan with a maturity of 5 years in which the first payment was on December 2016. Right after paying the first month on December 15, she made an advance payment for two (2) months and he intends to pay extra month every two months. In addition, she also dedicates his 13th month (13 month is equivalent to 2 & a half month) for an additional advance payment. Assuming that there are no late payments and everything goes well at what month and year will the loan matures?
Is the interest rate given?
When was the 13th month advance payment paid, Dec.15 or January 15?
The interest rate is not given, and the 13th month advance payment will be paid on January 15
Sorry, more details required.
The following details seem to be subject to interpretation. Please give your comments.
1. the advance payment in December is a prepayment for the next two months. Does that practice continue for the rest of the loan repayment?
2. Is the 13th month dedicated to repayment every year, or just the first year.
3. When does the first extra month repayment start, February 1st?
To determine the month and year when Sasha's car loan will mature, we need to calculate the total number of payments she will make.
Given that the car loan has a maturity of 5 years, and payments are made every month, we can calculate the total number of payments as follows:
Total Payments = 5 years * 12 months per year = 60 months
Now, let's break down Sasha's payment schedule:
1. First payment on December 2016: Sasha made the regular monthly payment on December 15, 2016.
2. Advance payment for two months: Right after the first payment, Sasha made an additional payment for two months, which covers January and February 2017.
3. Extra payment every two months: Sasha intends to make an additional monthly payment every two months. This means she will make an extra payment in April, June, August, October, December of each year.
4. Dedicates the 13th month for an additional advance payment: Sasha dedicates the 13th month (equivalent to 2 & a half month) to make an additional advance payment. This means she will make an additional payment in May of each year.
Let's calculate the total number of extra and advance payments Sasha will make:
Extra Payments: 60 months / 2 months (frequency of extra payment) = 30 extra payments.
Advance Payments: 60 months / 13 months (dedicating the 13th month for advance payment) = 4.62 advance payments. Since Sasha cannot make partial payments, we will round down to 4 advance payments.
Now, let's calculate the number of regular payments Sasha will make by subtracting the extra and advance payments from the total payments:
Regular Payments = Total Payments - Extra Payments - Advance Payments
Regular Payments = 60 - 30 - 4 = 26 regular payments
Finally, we add up all the payments to determine the month and year when the loan will mature from the first payment in December 2016:
Year of Maturity = 2016 (year of first payment) + 26 (number of regular payments) + 30 (number of extra payments) + 4 (number of advance payments) + 2.5 (dedicating the 13th month)
Year of Maturity = 2016 + 26 + 30 + 4 + 2.5
Year of Maturity = 2078.5
Therefore, the loan will mature in June 2078.