SOLUTION: Jessica borrowed $3300 from the bank in order to buy a new piano. She will pay if off by equal payments at the end of each week for 2 years. The interest rate is 8% compounded week

Question 1206588: Jessica borrowed $3300 from the bank in order to buy a new piano. She will pay if off by equal payments at the end of each week for 2 years. The interest rate is 8% compounded weekly. Determine the size of payments, and the total interest paid.
Found 3 solutions by Theo, math_tutor2020, ikleyn:
Answer by Theo(13342)   (Show Source): You can put this solution on YOUR website!
i used the ti-business analyst 2 calculator to get the detailed results.

inputs to that calculator were:

present value = -3300
future value = 0
number of weeks is 2 years * 52 = 104.
interest rate % per week = 8/52 = .153846154%.
payments are made at the end of each week.

calculator says that the payment at the end of each week needs to be 34.36124429 dollars.

that's the size of the payment required at the end of each week.

the total interest paid would be 104 * 34.36124429 = 3573.569406 minus 3300 = 273.5694063 dollars which you would round to 273.57 dollars.

i used excel to provide these results.

here's what it looks like.

Answer by math_tutor2020(3817)   (Show Source): You can put this solution on YOUR website!

The formula we use is
P = (L*i)/( 1-(1+i)^(-n) )
where,
P = weekly payment
L = loan amount
i = weekly interest rate in decimal form
n = number of weeks

In this case,
L = 3300
i = 0.08/52 since there are approximately 52 weeks in a year
n = 52*2 = 104

Lets find the weekly payment.
P = (L*i)/( 1-(1+i)^(-n) )
P = (3300*0.08/52)/( 1-(1+0.08/52)^(-104) )
P = 34.36124429157
P = 34.36
The weekly payments are $34.36

Side note: There are about 4 weeks in a month, so the monthly payment is 4*34.36 = 137.44

Jessica makes weekly payments of $34.36 for 104 weeks (aka 2 years)
She will pay back a total of 104*34.36 = 3573.44 dollars.

Subtract off the principal, aka amount loaned, to find the amount of interest
3573.44 - 3300 = 273.44

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Summary:
Weekly payment = $34.36
Total interest = $273.44

Answer by ikleyn(52900)   (Show Source): You can put this solution on YOUR website!
.

When you will solve this problem and will present it to the teacher,
make rounding for the month payment as tutor @math_tutor2020 does it.

So, the weekly payment is $34.36 dollars.

It is NOT 34.36124429 dollars, as tutor @Theo states - this value must be rounded
to become and to be a weekly payment.

Correspondingly, the payment for 2 years, or 104 weeks, is the value given in the post
by @math_tutor2020, i.e. 3573.44 dollars and not 3573.569406 dollars, as in the post by @Theo.

Correspondingly, the interest . . . and so on . . . I just tired to repeat.

Simply saying, when you solve the problem, make rounding of participating values
at a right place of the solution according to common sense and rules of rounding.

Be accurate and do not turn your job and your writing into mess.

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