Assume you invest $220 at the end of each year for 10 years at an annual interes

Question

Assume you invest $220 at the end of each year for 10 years at an annual interest rate of r. The amount of money in the account after 10 years is A = 220[(1+r)^10 - 1]/r. Your goal is to have $3248 in your account after 10 years. (a) Let f be the function such that f(x) = 220[(1+r)^10 - 1]/r. Using the Intermediate Value Theorem, determine whether there is an interest rate r in (0.01, 0.10), between 1% and 10%, that allows you to reach your financial goal. Choose the correct answer below. A. Yes, because f(0.01)

Explanation / Answer

From the given question,

f(x)=220[(1+r)10-1]/r

For maximum value of f(x), its derivative will be zero.

f '(x)=220{r[10(1+r)9]-[(1+r)10-1]}*1/r2=0

r[10(1+r)9]-[(1+r)10-1]=0

r=0.04

r=4%

Correct option is D

Yes, because the function is continous on [0.01,0.10] and 3248 is between f(.0.1) and f(0.10)

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