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Derive the approximation

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Reference no: EM131720814

If K dollars are charged now to a credit card on which interest is p% per year, then after t years, the balance will have grown to K(t)= K(1+ (p/100))^t

(a) Using linearization, show that ln(1 + (p/100) ) ≈ p/100 . (p is an interest rate, so p/100 is reasonably small)

(b) Derive the approximation ln(Kt) ≈ ln(K) + pt /100

(c) Approximate the percentage interest rate at which the balance doubles after 9 years. (your answer to (c) will contain a term involving ln(2))

Reference no: EM131720814

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