Question

Your favorite bank is offering to lend $10,000 to you with the agreement to make monthly payment of $250 over 4 years.

What is the effective annual rate the bank is charging you?

If you agree to borrow $10,000 with the above payment schedule, what would be the loan balance at the end of year 1.

Answer 1

Given about a loan,

Loan amount PV = $10000

Monthly payment PMT = $250

Year of loan = 4 years

so, monthly rate of interest can be calculated on financial calculator using following values:

PMT = -250

PV = 10000

N = 12*4 = 48

FV = 0

compute for I/Y, we get I/Y = 0.770

So, monthly rate = 0.770

So, effective annual rate = (1+monthly rate)^12 -1 = (1+0.77)^12 - 1 = 9.64%

So, effective annual rate bank charging is 9.64%

After 1 year, total number of period remaining = 3*12 = 36 months

With same monthly payment and same monthly rate, balance in the loan can be calculated using following values on financial calculator:

FV = 0

PMT = -250

N = 36

I/Y = 0.770

compute for PV, we get PV = 7833.95

So, Loan balance at the end of year 1 is $7833.95