SOLUTION: What monthly payment is required to amortize a loan of $50,000 over 10 years if interest at the rate of 6%/year is charged on the unpaid balance and interest calculations are made

Question 1200913: What monthly payment is required to amortize a loan of $50,000 over 10 years if interest at the rate of 6%/year is charged on the unpaid balance and interest calculations are made at the end of each month? (Round your answer to the nearest cent.)
Found 4 solutions by mananth, MathTherapy, math_tutor2020, ikleyn:
Answer by mananth(16946)   (Show Source): You can put this solution on YOUR website!
We are paying interest on the unpaid balance on a regular basis the formula needed is given by

P = payment amount
A = amount financed = 50000
r = decimal interest rate adjusted for periodicity 6% over 10 years
0.006 /month
n = total number of payments made 10 years 12 months 120 months

P= 50000 * 0.006/( 1 - (1+ 0.006)^ -120

= 300 / 1 ^ -120

= 300 / 1 - 1.006 ^-120
=300 / 1 - 0.487800581

=300 / 0.512199419

= $585.709

Answer by MathTherapy(10555)   (Show Source): You can put this solution on YOUR website!

What monthly payment is required to amortize a loan of $50,000 over 10 years if interest at the rate of 6%/year is charged on the unpaid balance and interest calculations are made at the end of each month? (Round your answer to the nearest cent.) Correct answer: $555.10

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

Answer: $555.10

Work Shown:

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

In this case
L = 50000
i = 0.06/12 = 0.005
n = 10*12 = 120 months

Then,
P = (L*i)/( 1-(1+i)^(-n) )
P = (50000*0.005)/( 1-(1+0.005)^(-120) )
P = 555.102509708256
P = 555.10

The answer can be confirmed with a calculator such as this one
https://www.calculator.net/loan-calculator.html

Answer by ikleyn(52844)   (Show Source): You can put this solution on YOUR website!
.

We need to keep a functioning team of tutors at this forum,
that will disprove wrong solutions posted by @mananth.

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