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How much should a new graduate pay in 10 equal annual payments, starting 2 years from now, in order to repay a $30,000 loan he has received today? The interest rate is 6% per year.

Respuesta :

Edufirst

Answer:

         [tex]\large\boxed{\large\boxed{\$4,579.84}}[/tex]

Explanation:

First, calcualte the how much is the principal two years from now using annual compound interest rate corresponfing to 6% per year. Then, use the formula that returns the constant periodic payment of a loan, assuming also annual compound interest of 6%.

1. Principal two years from now

  • Principal = Amount borrowed × (1 + r)ⁿ
  • r = 6%  = 0.06
  • n = 2 years
  • Principal = $30,000 × (1 + 0.06)² = $33,708

2. Monthly payment:

Formula:

       [tex]\text{Monthly payment}=\text{Principal}\times \dfrac{r(1+r)^n}{(1+r)^n-1}[/tex]

Substitute and compute

  • n = 10 years
  • principal = $33,708
  • r = 6% = 0.06

           [tex]\text{Monthly payment}=\text{\$33,708}\times \dfrac{0.06(1+0.06)^{10}}{(1+0.06)^{10}-1}[/tex]

          [tex]\text{Monthly payment}=\$4,579.84[/tex]

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