Question

If you buy a computer from manufacturers for 2565 and agree to repay it in 36 equal installments at 1.83% interest per month on the unpaid balance how much are your payments? How much total interest will be paid?

Answer 1

INFORMATION:

We know that:

- you buy a computer from manufacturers for 2565

- you agree to repay it in 36 equal installments at 1.83% interest per month on the unpaid balance

And we need to calculate how much will the payments be and how much will be paid in total in interest

STEP BY STEP EXPLANATION:

Since we need to calculate the amount of each periodic payment, we must use the next formula

Where,

- pv (present value) = The starting balance in an account. This number can be zero, positive (when you take out a loan), or negative (when you make a deposit).

- fv (future value) = The ending balance after the specified number of payment periods (np).

- np (number of periods) = The number of payment periods, usually expressed in months.

- pmt (payment) = The amount of each periodic payment, usually a negative amount.

- ir (interest rate) = The per-period interest rate on the account.

Now, analyzing the given information we know that:

- pv = 2565

- fv = 0 (at the end we will paid all the price of the computer)

- np = 36

- pmt = we must calculate it

- ir = 1.83%

Then, replacing the values in the formula and simplifying

`pmt=(0.0183(0+2565(0.0183+1)^(36)))/((0.0183+1)^(36)-1)=-97.91`

The negative symbol is because it is money that will be paid.

That means, Payments will be $97.91

Finally, to calculate the total paid on interest we need to calculate the total paid and then we must subtract the initial value to total

`\text{ Total paid}=97.91*36=3524.76`
`\text{ Total paid-Initial value}=3524.76-2565=959.76`

So, the total paid on interest will be $959.76

ANSWER:

- Payments will be $97.91

- The total paid on interest will be $959.76