Suppose dollar 300 was deposited into one of four bank accounts and t is time in
ID: 3014333 • Letter: S
Question
Suppose dollar 300 was deposited into one of four bank accounts and t is time in years. Describe how the balance is growing each (without computations) just by giving the nominal rate and how often the interest any is being compounded. B = 300 (1.05)^t B = 300(0.8)^t B = 300 (1.01)^12t B = 300(0.94)^2t B = 300e^0.2t By evaluating these expressions at t = 1, we see we are multiplying dollar 300 by 1.05, (1.01)^12, etc. What role do these numbers play in each of these exponential models? Do you still agree with the descriptions you gave in the items above?Explanation / Answer
B should be of the form: B = 300[1 + r/n]nt
where n is the number of times the interest is compounded annually.
a] B = 300[1.05]t
=> B = 300[1 + 0.05]t
here, n = 1 and so the interest is compounded annually with the rate of 5% and the balance will appreciate since 1.05 > 1
b] B = 300[0.8]t
Compounding is done annually with the rate of 20% and the balance will depreciate.
c] B = 300[1.01]12t
=> 300[1 + (0.12/12)]12t
so, the interest is compounded monthly with the rate of 12% and the balance will appreciate.
d] B = 300[0.94]2t
=> B = 300[1 - (0.12/2)]2t
so, the interest is compounded semi annually with the rate of 12% and the balance will depreciate.
e] B = 300e0.2t
here, the interest is compounded continuously and the balance will appreciate.