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Kyle borrows $25000 at 6% p.a. simple interest for four years. Calculate the monthly repayment required to pay this loan off in 48 equal instalments.

Sagot :

semsee45

Answer:

$587.13

Step-by-step explanation:

Monthly Payment Formula

[tex]\sf PMT=\dfrac{Pi(1+i)^n}{(1+i)^n-1}[/tex]

where:

  • PMT = monthly payment
  • P = loan amount
  • i = interest rate per month (in decimal form)
  • n = term of the loan (in months)

Given:

  • P = $25,000
  • i = 0.005
  • n = 48

To calculate i, divide the interest rate per annum by 12 and convert to decimal form:

[tex]\implies \sf i=\dfrac{6\%}{12}=\dfrac{0.06}{12}=0.005[/tex]

Substitute the given values into the formula and solve for PMT:

[tex]\implies \sf PMT=\dfrac{25000 \cdot 0.005(1+0.005)^{48}}{(1+0.005)^{48}-1}[/tex]

[tex]\implies \sf PMT=\dfrac{125(1.005)^{48}}{(1.005)^{48}-1}[/tex]

[tex]\implies \sf PMT=587.1257262...[/tex]

Therefore, the monthly repayment required to pay this loan off in 48 equal installments is $587.13 (nearest cent).

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