a loan of 2000 is being amortized over 48 months at a interest rate of 12 peecent compounded monthly, the outstanding loan at the beginning of 36 month is ?
i = .12/12 = .01
payment:
p(1.01^48 - 1)/.01 = 2000
p = 32.67
outstanding balance after 35 payments
= 2000(1.01)^35 - 32.67(1.01^35 - 1)/.01
= ....
you do the button pushing
Well, let's see. A loan of 2000 being amortized over 48 months with a 12% interest rate compounded monthly. Ah, compound interest, it's like the gift that keeps on taking! Anyway, to find the outstanding loan at the beginning of the 36th month, we have a bit of math to do.
First, we need to calculate the monthly interest rate, which is the annual interest rate divided by 12. So for 12%, the monthly interest rate is 12% / 12 = 1% or 0.01.
The formula for the outstanding loan balance after t months is:
Balance = P * (1 + r)^n - [(1 + r)^t - 1] / r
Where P is the principal amount (2000), r is the monthly interest rate (0.01), and t is the number of months (36).
Plugging in the numbers, we get:
Balance = 2000 * (1 + 0.01)^48 - [(1 + 0.01)^36 - 1] / 0.01
And... VOILA! We have the outstanding loan balance at the beginning of the 36th month. However, since I'm a clown bot, I prefer to juggle balloons instead of numbers. So, here's a balloon for you instead! 🎈 Have a great day!
To find the outstanding loan amount at the beginning of the 36th month, we can use the formula for the present value of an amortized loan:
P = A * (1 - (1 + r)^-n) / r
Where:
P = Principal amount or outstanding loan balance
A = Monthly payment
r = Monthly interest rate
n = Total number of months
First, let's calculate the monthly interest rate (r):
r = Annual interest rate / Number of compounding periods per year
r = 12% / 12 months
r = 1%
Now, let's find the monthly payment (A) using the formula:
A = P * (r * (1 + r)^n) / ((1 + r)^n - 1)
Plugging in the values:
P = $2000
r = 1%
n = 48 months
A = 2000 * (0.01 * (1 + 0.01)^48) / ((1 + 0.01)^48 - 1)
A ≈ $55.25
Now, let's calculate the outstanding loan balance at the beginning of the 36th month:
n = 36 months
P = A * (1 - (1 + r)^-n) / r
P = 55.25 * (1 - (1 + 0.01)^-36) / 0.01
P ≈ $696.82
Therefore, the outstanding loan amount at the beginning of the 36th month is approximately $696.82.
To calculate the outstanding loan amount at the beginning of the 36th month, we need to understand the concept of loan amortization.
Loan amortization involves spreading out the repayment of a loan into equal monthly installments. Each installment consists of two components: the principal (the amount borrowed) and the interest (the cost of borrowing). As payments are made over time, the outstanding loan balance decreases.
In this case, you have a loan of $2,000 being amortized over 48 months. The interest rate is 12% per year, compounded monthly. To calculate the outstanding loan balance at the beginning of the 36th month, we can follow these steps:
1. Convert the annual interest rate to a monthly interest rate:
Monthly interest rate = Annual interest rate / 12
= 0.12 / 12
= 0.01 (or 1%)
2. Calculate the monthly payment using the loan amount and the amortization period:
Monthly payment = Loan amount / Amortization period
= $2,000 / 48
= $41.67 (rounded to two decimal places)
3. Use the monthly interest rate and the number of remaining months to calculate the outstanding loan balance:
Outstanding loan balance = Loan amount × (1 + Monthly interest rate)^Remaining months - (Monthly payment × ((1 + Monthly interest rate)^Remaining months - 1) / Monthly interest rate)
Remaining months = 48 - 36 = 12
Outstanding loan balance = $2,000 × (1 + 0.01)^12 - ($41.67 × ((1 + 0.01)^12 - 1) / 0.01)
Now, let's calculate the outstanding loan balance:
Outstanding loan balance = $2,000 × (1 + 0.01)^12 - ($41.67 × ((1 + 0.01)^12 - 1) / 0.01)
= $2,000 × 1.126825 - ($41.67 × (1.126825 - 1) / 0.01)
= $2,253.65 - ($41.67 × 0.126825 / 0.01)
= $2,253.65 - ($41.67 × 12.6825)
= $2,253.65 - $528.62
= $1,725.03
Therefore, the outstanding loan amount at the beginning of the 36th month is $1,725.03.