Mrs. Smith borrowed $20,000 from Last National Bank. She will repay the loan with 5 annual payments and her interest rate is 14%. a) Find the amount of her annual payments. b) What is her loan balance after she has made her 3rd annual payment?
Use the amortization tool at
http://www.bretwhissel.net/cgi-bin/amortize
The annual payment amount is 5825.67
There is also a formula you can use, but it is rather hard to memorize. You find it at
http://www.vertex42.com/ExcelArticles/amortization-calculation.html
To find the amount of Mrs. Smith's annual payments, we can use the formula for calculating the periodic payment on an installment loan. This formula is:
P = (r * PV) / (1 - (1 + r)^(-n))
Where:
P is the periodic payment,
r is the interest rate per period,
PV is the present value or loan amount, and
n is the number of periods.
In this case, Mrs. Smith borrowed $20,000, so PV = $20,000. The interest rate is 14%, or 0.14, and she will make 5 annual payments. Therefore, n = 5.
Let's plug these values into the formula to find the amount of her annual payments:
P = (0.14 * $20,000) / (1 - (1 + 0.14)^(-5))
P ≈ $5,046.74
So, Mrs. Smith's annual payments will be approximately $5,046.74.
To find Mrs. Smith's loan balance after she has made her 3rd annual payment, we need to calculate the remaining loan balance using the remaining number of payment periods.
To do this, we will use the formula to calculate the remaining loan balance on an installment loan, which is:
RB = PV * (1 + r)^n - P * ((1 + r)^n - 1) / r
Where:
RB is the remaining loan balance,
PV is the present value or loan amount,
r is the interest rate per period,
n is the remaining number of periods, and
P is the periodic payment.
In this case, after Mrs. Smith has made 3 annual payments, the remaining number of payment periods will be 5 - 3 = 2.
Let's plug these values into the formula to find her loan balance after the 3rd annual payment:
RB = $20,000 * (1 + 0.14)^2 - $5,046.74 * ((1 + 0.14)^2 - 1) / 0.14
RB ≈ $13,838.89
Therefore, Mrs. Smith's loan balance after she has made her 3rd annual payment will be approximately $13,838.89.