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SAM Metal Works, Inc. borrowed $16,000 from its bank and will repay $21,000 in 9 year(s), interest compounded annually. Determine the interest rate at which SAM Metal Works borrowed the money. (Note: When entering Time Value of Money problems with two dollar amounts, one of the amounts must be negative. For this problem, use the drop-down to add the "+/-" button as a keystroke immediately before PV.)

Respuesta :

Answer:

3.07% is the rate SAM metal work borrowed the money for.

Explanation:

Given : future value of $210000 after 9 years

             present value of $16000 which is borrowed now.

              the period which is 9 years compounded annually

              therefore we want to find the interest  rate at which the loan has matured to $21000 therefore  we will use the formula for future value in compounding interest which is [tex]Fv = Pv(1+i)^n[/tex]

where Fv is the future value of $21000

Pv is the present value of $16000

i is the interest rate charged which what we are looking for

n is the period of the in which the loan takes to be $21000.

then we substitute into the formula:

  [tex]$21000 = $16000(1+i)^9[/tex] then divide both sides with $16000 to solve for i

21000/16000 = (1+i)^9 e multiply the period by 1/9 to make it 1 so we multiply both sides on the exponents.

(21000/16000)^(1/9) = (1+i)^9x(1/9) thereafter we transpose 1 to solve for i

((21000/16000)^(1/9))-1= i then we compute the solution

0.030675x 100 = i

therefore the interest rate is 3.07%.

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