You invest $900 today and receive a $100 coupon payment at the end of every year for 5 years. In addition, you receive $1,000 at the end of year 5. What is the interest rate?
PV = -900 FV = 1,000 N = 5 PMT = 100 CPT I --> I = 12.83%
My question is, what does the 12.83% represent here? Intutively, when the calculator solved for 12.83%, is it finding the rate that takes $900 at t = 0, pmts in years 1 to 5, and then calculates 12.83% on what basis?
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Had I seen this problem on the exam, I would have probably known how to solve it, but I cannot guarantee that I would know how to interpret it and that is one of my concerns. Any help would be appreciated to put this answer into simple layman terms, or even if you would like to prove it mathematically.
12.83% represents the rate of return that you are earning each period (each year in your example).
To see this, you should create an amortization table in Excel. You start year 1 with $900 and add 12.83% interest, or $115.47, giving you $1,015.47 at the end of year 1. You deduct $100 (the payment you receive), so you end the year with $915.47.
You repeat the process in year 2, starting with $915.47, then repeat it in years 3, 4, and 5. Note that in year 5 you’ll deduct $1,100 (= $100 + $1,000). If you’ve done it correctly, your account balance at the end of year 5 should be zero.
I’m trying to think of the intuitive approach, if I invest $900, and earn interest on that $900, and then receive a payment of $100, I’m not sure why I would deduct the payment from the interest received on my initial outflow? I think I’m missing a core idea here, or maybe I just don’t understand what I’m trying to calculate in the first place …
I pay $900 today (outflow)
For 5 years the financial institution will pay me at the end of each year $100 (inflows)
At the end of the 5th year, I will also receive $1000 (inflow)
In general, I understand that an amortization table is constructed when you take out a mortgage for example, your payments are split into (return of interest, and return of principle) and accordingly principal at beginning of year is equal to principal beginning of period - return of principal).
But this example is weird, it goes against this logic or my logic at least.
Suppose that you invest $1,000 in a bank account today, and in one year you close the account, removing $1,070. What was your annual rate of return?
Seven percent. Your $1,000 increased by $70 in one year, and $70 / $1,000 = 0.07 = 7%.
Suppose that you invest $1,000 in a bank account today, in one year you remove $50, and in two years you close the account, removing $1,050. What was your annual rate of return?
Five percent. Your $1,000 increased by $50 in the first year. You removed the $50, leaving $1,000. That $1,000 increased by $50 in the second year, and you removed $1,050.
That’s exactly what you’re doing in the amortization table. Your account balance each year is increasing by 12.83%. You remove some of it ($100) and leave the rest to continue to grow at 12.83%. At the end of 5 years you close the account and remove $1,100.
By the way, you’re not looking for an intuitive approach; you’re looking for understanding (i.e., logic).