Question 1167594: A person borrows $1,950 on a bank credit card at a nominal rate of 18% per year, which is actually charged at a rate of 1.5% per month.
(a)
What is the annual percentage yield (APY) for the card? (Round your answer to one decimal place.) I got 19.56 percent
b)
Assume that the person does not place any additional charges on the card and pays the bank $150 each month to pay off the loan. Let
Bn be the balance owed on the card after n months. Find an explicit formula for
Bn. ok so I got 1,950(1.015)^n-150n however the website where i do my homework says its wrong and i need the answer to part b so that i can solve part c,
so what did i do wrong in part b?
c How many months will be required to pay off the debt? (Round your answer up to the nearest whole number.)
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! A person borrows $1,950 on a bank credit card at a nominal rate of 18% per year, which is actually charged at a rate of 1.5% per month.
a) What is the annual percentage yield (APY) for the card? (Round your answer to one decimal place.) I got 19.56 percent
your answer is correct except you rounded to two decimal places.
the answer would be 19.6% if you rounded to 1 decimal place.
b) Assume that the person does not place any additional charges on the card and pays the bank $150 each month to pay off the loan.
Let Bn be the balance owed on the card after n months.
Find an explicit formula for Bn.
i don't think you have the right formula.
the right formula is:
Bn = p*(1+r)^n-a*(((1+r)^n-1)/r)
Bn is the remaining balance on the loan.
p is the present value of the loan.
r is the interest rate per month.
n is the number of months.
a is the monthly payment at the end of each month.
c) How many months will be required to pay off the debt? (Round your answer up to the nearest whole number.)
the formula to use to solve for this is:
n = ln(a/(a-r*p))/ln(1+r)
n = the number of months required to satisfy the loan.
a is the payment made at the end of each month.
p is the present value of the loan (how much you borrowed)
r is the interest rate per month.
ln is the natural log function on your scientific calculator.
when a = 150 and p = 1950 and r = .015, the formula becomes:
n = ln(150/(150-.015*1950))/ln(1+.015)
solve for n to get n = 14.56905414
that's the number of months required to pay off the loan completely.
round that to the nearest integer to get n = 15.
now that you know what n is, you can confirm the value is correct by applying it to the remaining balance on the loan formula.
that formula was shown in part b.
it is:
Bn = p*(1+r)^n-a*(((1+r)^n-1)/r)
when p = 1950 and r = .015 and n = 14.56905414 and a = 150, that formula becomes:
Bn = 1950*(1+.015)^14.56905414-150*(((1+.015)^14.56905414-1)/.015).
solve for Bn to get:
Bn = 0
a remaining balance of 0 means the loan has been paid off.
you could have used the Bn formula to find the number of months required to pay off the loan but you would have had to repeat the calculations several times before narrowing the solution down.
the n formula frees you from doing all those iterations and allows you to find the value of n in one shot.
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