Terry Martinez is considering taking out a loan to purchase a desk. The furnitur

Question

Terry Martinez is considering taking out a loan to purchase a desk. The furniture store manager rarely finances purchases, but will for Terry “as a special favor.” The rate will be 10% per year, and because the desk costs $600, the interest will come to $60 for a one-year loan. Thus, the total price is $660, and Terry can pay it off in 12 installments of $55 each.
Use the interest rate of 10% per year to calculate the net present value (NPV) of the loan? Based on this interest rate, should Terry accept the terms of the loan.

I was provided with the answer, which is $-25.60.
I would like to see the steps that get me to that answer

Explanation / Answer

Let me explain you by an example, I hope it will be helpful for you. Suppose, for example, you have $100 in your pocket. If you put that money intoa savings account that earns 10% per year, paid annually, then you would have$100 x 1.1 = $110 at die end of the year. At the end of two years, the balance in theaccount would be $110 plus another 10%, or $110 x 1.1 =$ 121. In fact, you can seethat the amount you have is just the original $100 multiplied by 1.1 twice:$121 =$100 x 1.1 x 1.1 =$100 x l.l2. If you keep the money in the account forfive years, say, then the interest compounds for five years. The account balance wouldbe $100 x l.l5 = $161.05. We are going to use this idea of interest rates to work backward. Suppose, for ex-ample, that someone promises that you can have $110 next year. What is this worthto you right now? If you have available some sort of investment like a savings ac-count that pays 10% per year, then you would have to invest $100 in order to get$110 next year. Thus, the present value of the $110 that arrives next year is just$110/1.1 = $100. Similarly, the present value of $121 dollars promised at the endof two years is$121/(l.l2) = $100. In general, we will talk about the present value of an amount x that will be re-ceived at the end of n time periods. Of course, we must know the appropriate inter-est rate. Let r denote the interest rate per time period in decimal form; that is, if theinterest rate is 10%, then r = 0.10. With this notation, the formula for calculatingpresent value (PV) is PV(a-, n, r) ¦¦ (1 + r)" The denominator in this formula is a number greater than 1. Thus, dividing x by(1 + r)" will give a present value that is less than x. For this reason, we often saythat we "discount" x back to the present. You can see that if you had the discountedamount now and could invest it at the interest rate r, then after n time periods (days,months, years, and so on) the value of the investment would be the discountedamount times (1 + r)", which is simply x. Keeping the interest rate consistent with the time periods is important. For exam-ple, a savings account may pay 10% "compounded monthly." Thus, a year is really 12time periods, and so n = 12. The monthly interest rate is 10%/12, or 0.8333%. Thus,the value of $100 deposited in the account and left for a year would be$100 x (1.00833)12 = $110.47. Notice that compounding helps because the interestitself earns interest during each time period. Thus, if you have a choice among sav-ings accounts that have the same interest rate, the one that compounds more fre-quently will end up having a higher eventual payoff.

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