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Usimov
9 days ago
8

Hugh akston took out a 30 year mortgage with an ear of​ 5.9%. if hugh borrowed​ $300,000 to buy his​ home, then his monthly paym

ent will be closest​ to:
Business
2 answers:
soldi70 [3.1K]9 days ago
7 0
The formula for calculating the present value of an ordinary annuity is
Pv=pmt [(1-(1+r/k)^(-kn))÷(r/k)]
With the present value set at 300000
PMT is the amount for monthly payments?
R is the interest rate at 0.059
K indicates monthly compounding, which is 12 as payments are made monthly
N represents the time period of 30 years
To derive the formula for PMT
PMT=pv÷ [(1-(1+r/k)^(-kn))÷(r/k)]
PMT=300,000÷((1−(1+0.059÷12)^(
−12×30))÷(0.059÷12))
=1,779.41
Scilla [3.2K]9 days ago
3 0

Result:

Monthly payment = $1,779.41

Clarification:

A mortgage is a type of loan that is secured against a specific property, with payments made periodically over a set duration.

Below is the formula for determining Hugh's monthly payment

\\P[\frac{r(1+r)^n}{((1+r)^n)-1)}]

Definitions of the terms below

  • P = Amount of loan.
  • M = Monthly repayment of the mortgage.
  • r = Interest rate, which must be adjusted for monthly calculations. Thus monthly rate[5.9% expressed as a decimal] = \frac{0.059}{12} = 0.004917
  • n = Count of payments, equating to the loan duration. Hence N = 30 years multiplied by 12 months = 360.

Applying this to the formula yields:

\\300000 * \frac{0.004917(1+0.004917)^'360'}{(1+0.004917)^'360'}-1

Which results in a monthly payment of $1779.41

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