## Related questions with answers

You take out a 2-year, $5,000 loan at 9% interest with monthly payments. The lender charges you a$100 fee that can be paid off, interest free, in equal monthly installments over the life of the loan. Thinking of the fee as additional interest, what is the actual annual interest rate you will pay?

Solution

VerifiedLet's first compute the payments without the fee. We are given the following information:

$\begin{aligned} & t = 2\\ & PV = \$5,000\\ & r = 9\% = 0.09\\ & m = 12\\ & i = r/m = 0.09/12 = 0.0075\\ & n = mt = 24 \end{aligned}$

We can now use the payment formula for an ordinary annuity (a loan can be regarded as an annuity from lender's perspective).

$PMT = PV\dfrac{i}{1-(1+i)^{-n}} = 5,000\times\dfrac{0.0075}{1-(1+0.0075)^{-24}} = \$228.42$

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