math homework payments

Question

Rounding in the calculation of monthly interest rates is discouraged. Such rounding can lead to answers different from those presented here. For long-term loans, the differences may be pronounced.

You borrow $15,000 with a term of four years at an APR of 6% to buy a truck. What is your monthly payment? (Round your answer to the nearest cent.)

$ 

How much total interest is paid? (Round your answer to the nearest cent.)

$ 

Answer 1

Monthly Payment Auto

a=p*r/12(1+r/12)^n/((1+r/12)^n)-1)

a-monthly pay

p-principal

r-int/mo

n-months

a=15,000*.06/12(1+.06/12)^48/((1+.06/12)^48-1)=$315.70/mo

Answer 2

This can be done several ways depending on the technology available to you. You would need, at the very least, a calculator that can raise numbers to powers easily. If you have a calculator with TVM (time value of money) functions, such as TI-83 and TI-84 or TI-BAII Plus or any business calculator, then it has internal functions that make this pretty easy. I'll show you how to do it with the TVM or without the TVM.

Without TVM:

Present Value = Payment · (1 - (1 + i)^-n) / i

where i is the interest rate per compounding period and n is the number of compounding periods.

In our case, we know the present value (15,000), the interest rate (0.06/12 = 0.005 because we assume that it compounds with the same frequency as the payments, which are monthly), and the number of interest periods (4 · 12 = 48 months). We don't know the payment amount, so we can put in a variable R for that, which we can then solve for.

15,000 = R · (1 - (1 + 0.005)^-48) / 0.005

15000 = 42.58032R

R = 352.28

With TVM:

TVM calculators can vary a little bit, but generally they have fields for present value (PV), payment (PMT), interest (I/Y), number of periods (N), and future value (FV).

In this case, we are not concerned with future value (FV), so nothing goes in that field.

We are also not putting in anything for payment (PMT) because we don't know it yet.

Here's what we need to enter:

N=48

I%=0.5

PV=15000

The PMT field is the one to calculate. On the TI-83 and TI-84, this is done by moving to that field and hitting ALPHA ENTER (which is SOLVE), and you will see -352.2754357. You might think that you made a mistake because it produced a negative number. However, the negative sign indicates that the cash flow is going in the opposite direction from the present value. The PV is what goes from the lender to the borrower to purchase the truck. The PMT goes from the borrower to the lender, which is the opposite direction, so it has the opposite sign.

Either way, the answer is $352.28.

The total interest paid can be calculated by calculating how much money was paid to the lender and subtracting the value of the loan.

352.2754357 · 48 = 16909.22

16909.22 - 15000 = $1909.22 of total interest